I do not think all razors benefit from a concave bevel.
I'm a devout man of science, and believe it is hard to entirely remove one's biases when evaluating something so highly subjective as the quality of a shave.
Long ago, in my many years strictly adhering to well-established forum doctrine that razor bevels were meant to be flat/flush 2/3rds of triangles, I used to use a friendly neighbor's name and address to mail a small army of all-the-same Dovo 'Best Quality' black handled entry level Solingens to be honed post-factory by various "honemeisters" of the forums. I'd mark scales with infrared pen as to honer, stirred in some of my own, and some factory edges, too. I evaluated them not knowing who's who...shave with each at least twice, jot some subjective evaluations, break out the blacklight and find out who's edge is from who. What I found was my edges were rarely extraordinary, one guy [from New England, & still in the business today] consistently had the best results, and factory fresh Dovos often rated better than many "honemeisters".
When you don't know who is who, it is a much more honest evaluation.
Now that I am doing this silly concave bevel shaping stuff, I can't really do blind evaluations, as it is obvious when I look at the razors if they've been meaningfully concaved - I know what to look for and can't "Jedi Mind Trick" it away from observation. Short of busting out the sleep mask for shaving [where as it turns out having done so a few times, making lather's the real hard part, also the mask gets in the way], confirmation biases we all suffer are unavoidable.
So for me, the subjective metric I find most effective for "Will THIS razor benefit from a concave bevel?" is the thumbnail interaction test. Think of bringing your razor edge down to press upon your thumbnail, and watching how the bevel moves from the pressure then returns to form entirely unharmed when you take the thumbnail away. In this regard, the more easily the razor bends with little pressure and great immediacy and the further it seems to move without issue, I associate having best 'electric' improvement of blade feel on the face. When you concave a bevel on a good razor, it will bend further via that test, and more quickly, with less force.
In that regard, I cannot recommend late era extra hollowed Sheffield razors enough, nothing works as well I've tried. They had some sort of unique heat treatment back then [which was reputedly also very bad for the operators' lifespans], involving lead and ash stirred into water and repeated heat/forge/quench/reheat/reforge cycles. Whatever the special sauce, they're supremely flexible steels highly resistant to chipping, and their later stuff's also extremely thinly ground, so they're for me kings of this concave razor taboo. Only problem is, finding them 6/8"+, extra hollow, lots of meat on the bone end to end, zero issues with pitting/chipping/rust...kind of a long hunt on eBay, and while still cheaper than new razors where labor's not been paid many times over for the tool's creation, not what I call a great bargain. But they're the best of what I've tried, and bargains are out there for the patient, so if you enjoy eBay hunting as a hobby, nothing finer likely exists nor ever will.
Modern Solingens, certainly they benefit, especially 6/8"+ without shoulder, like the standard Bismarck. Maybe if I had smaller wheels shapes I could unearth more benefit from common 5/8" Solingen round head carbon steel shouldered blanks, but I still say those work better for my face than flat bevels if the abrasives are identical, just not eye-poppingly so like on any 6/8". Exception is 5/8" no-shoulder Spanish head razors like Bergischer Löwe; those, already much thinner than the standard style 5/8" Solingen, their improvement's anything but subtle, and I own a lot of them.
Vintage late Victorian / early 20th. c. USA blades, excellent response.
Vintage Swedish between-the-wars, they're already so thinly ground and actuely beveled that yes, I do say to thin the bevel a little, but they're very chippy-prone razors, so better to only add a little concavity and finish on a flat, or alternatively, thin the bevel a lot and finish on a conCAVE hone or on a pasted paddle/hanging strop (also concave, which means the tip of the bevel will be convex, backed by a concave remainder to the bevel, best of both worlds).
Modern French-forged respond brilliantly. You can concave them vs much shorter diameters, at least Thiers-Issard, and they hold the concave position easily, no chipping, electric improvement in blade action. No issues shaping bevels vs 6.5'Ø all the way through to apex, which means if I had a 1mØ or even smaller wheel(s), I could've used them for the TIs' back-bevel zones, and something longer up at the apex, and get even more metal removed from the bevel w/o any chipping issues. Goal as I see it is remove as much metal in the bevel as the razor allows w/o chipping.
Portland Razor Works & Hart Steel, while I think they're not as good a product as the high watershed Gold Dollar specimens, I have honed-for-hire a few and had heard back from the customers "it never shaved this well before", multiple times.
Razors that are super thinly ground and very hard, like Wacker, don't seem to change much for me on my face. However, I have a customer that's a retired miner and he has lots of cool toys (he's even seen a Pike Hard Ark wheel!) owns the costly stuff like Tim Zowada, Max Sprecher, etc., he's a very private man that absolutely abhors these shaving forums. To a razor, he's said to me many times in emails how much better they work when he concaved their bevels. His preference for ultra hard & thin razors is to finish all the way to concavity (no flat steps at the end) with diamond films on PSA which are placed atop wooden blocks he's shaped via the taboo concave lapping plate, then he uses abrasive sprays upon balsa wood blocks, also shaped convex. He's even mentioned it in passing to Mr. Zowada at a tradeshow, that Mr. Z's own ~$1000 item worked much better for him when he changed it this way, but Mr. Z. just dismissed it and praised his flat JNats. Mr. Zowada suffers no shortage of customers to buy his razors vs his available labor, Mr. Sprecher either, so they must be doing something right regardless of their bevels' shapes. Mr. Sprecher's one of the odd ones, like the fine real doctor in Minnesota and the not-an-emm-dee "Dr. Matt", that actually own the lapping plate but won't dare seem to use the thing, too busy to shape a stone I guess. I prefer those devoted chaps who dismiss out of hand and would not also buy one, for it doesn't make any sense to me to buy a tool and never use the tool for its intended purpose.
I've only honed one frameback razor this concave bevel way, from someone that sent one in for paid honing. A very stiff razor from Japan made in their post WWII era. Didn't hear back, so don't know if he liked or not. Doesn't seem on paper a great candidate, because ignoring their typically hard steel, behind the bevel plane they reach their maximum thinness immediately - they're not like fishing rods getting thinner and thinner progressively as you move from the spine to apex. So, they may not flex differently, or at all. Like a DE blade, they make their living via superior overall thinness at a point far behind the apex.
I've deliberately tried to induce bevels to chip from concaving, and mostly been unsuccessful. Ignoring Chinese razors, for my own stable of ~50 razors, twice I've seen it, but one was a stainless Solingen 5/8", kinda shouldn't count. The other is one particular specimen of carbon 5/8" no-shoulder Spanish head modern Solingen, and a specimen which was notably looking more ground thin from the factory, and only at the last <3mm right near where the cutting edge ends at the heel. So while the ~2mØ shape is to me a great tool for improving the comfort of almost any razor, it isn't as good as having a wheel made of an extremely fine abrasive, a wheel slow enough in its rotations and cooled with water or oil to preserve the razor's heat treatment, and a wheel small enough in its diameter that at all points of bevel refinement you would use it freehand, spine off the stone. If I had that, I could on the fly alter the approach of the bevel to the wheel by feel, and the amount of bevel depth interacting with the wheel as well as the pressure imparted, to have an extremely complex compound form to a concave bevel. But those options were lost to time. I would love a shorter diameter at my disposal to start up 4/8" and 5/8" razors better, but shapes cost $, and shorter diameters cost more off the corners of a stone (on a 2x4" a 1x8mØ shape costs -2.7mm, and -6mm off a 2x6"!)
This is not a NEED thing. Not everyone will need a concave bevel. Not everyone will notice a difference. Not everyone will even like it better. But they're intended to be made that way, however slightly, by the current producers, and it is mentioned in old grinding textbooks, and the very old grinder told me 14yrs ago that nothing compared to the on-the-fly compound concave bevel off a Pike Ark wheel. Take that for what it is worth to you, but if you've struggled with using a straight razor in any way after devoutly adhering to the constant refrain here and elsewhere that only a flat flush bevel is correct, you may wish to try a different path espoused by the producers of the tools. It is kind of like comparing summer tires to all season tires here in FL, or MC cartridges to MM cartridges on a turntable, or for that matter comparing turntable music vs digital music from the same amplifier/speakers/room. My wife firmly states she hears no differences. My 15yr old daughter, gifted and interested in music, says she hears a clear difference. I (thought I) heard a difference adopting to a turntable lifestyle, and (thought I) heard a difference when I switched to MC cartridges vs MM, and (thought I) heard a difference incorporating a step-up transformer in the signal path. The biggest endorsement for myself and the concave bevels is that prior to switching, I'd given up on coticules shaving me well; just not sharp enough at the apex they could make...but now, when that same sharpness-limited apex is backed by significantly thinner steel, I love coticules again.
. Oh, in case you were confused about the bottom photo, that is called a hone. Probably a very flat one. If needed, we could assist you with instructions on how to use one.
