The quick blade installation was in the fact that all you had to do to change blades was to twist a TTO open and then closed, as opposed to disassembling a 3-piece razor, placing the blade on the cap, aligning the cap with base, and screwing on the handle.
While they made the speed of loading the blade even faster, it was the difference in speed between the TTO and the 3-piece that made them call it "Superspeed". Of course it wasn't the first TTO design, but all TTOs were specifically marketed for the speed of loading and unloading the blade, not shave speed.
Here's some text copied from Gillette's original advertising brochures from Mr. Razor site, for various TTO razors.
1936 Aristocrat
"Just twist the handle and the head opens, allowing you to remove or replace the blade in a second. Twist again,
the razor head shuts and you are ready for another perfect shave. Here is speed and convenience for either change of blade or
cleaning after shaving."
1938 Aristocrat
"Think of the convenience of this "one-piece" Razor. Think of the time it saves."
1943 Ranger Tech:
"A twist-it's open; a twist—it's closed. The most convenient and fastest shaving razor ever produced. No loose parts to get
lost. Easily cleaned, simply hold under faucet."
1939 Popular #45
"The Gillette 'one-piece' razor brings shaving down to its simplest terms.
No bits or pieces to screw or unscrew. Just twist the handle —the head opens for cleaning or a new blade. Twist again-and it's ready for your next shave. Even if you already have a Gillette you should get yourself a 'one-piece' razor. It will save you time and trouble — and give you a quicker, cleaner, more comfortable shave than you've ever had before!"
1943 Ranger Tech
"A twist-it's open; a twist—it's closed. The most convenient and fastest shaving razor ever produced."
And, finally, 1948 Superspeed (the emphasis is as it appears in the ad)
"This is the only razor that combines instant blade changing with double edge economy."
So as you can see, the speed of blade change is a recurring theme here. Not the speed of shaving. Gillette consistently marketed their TTO razors as being the fastest to change blades, and one model eventually got called "Superspeed".