'Fast is Fast' as a phrase has the same failing that 'slow is smooth, smooth is fast' does, and it's obvious that it was developed as a counter to an existing school of thought.
Both schools have the same goal: Speed and Accuracy
The question of start fast or start slow, can be argued, legitimately, as long as no one forgets or fails to understand that it's the shared goal that is critically important to survival.
Are you a student of history or bad movies? Acolytes who start to set rules for whom their master is allowed to associate with tend to meet bad ends.
I started slow, for 10 years anyway. In that time, I'd not shot in matches, just lazily playing at the range shooting tiny little groups like most people.
Then I was taught how to stay alive with a handgun in 81. The rules changed that week for me. No more slow lazy days at the range plinking tiny little groups as I was working the streets and would be working with that group of people from time to time overseas in some nasty biz.
From that moment I got back from the compound, it was train to speed of draw to hits, speed of split times. So I started that road not as a novice, but shooting in a manner that would not afford me much life expectancy in the games I was playing and would be playing in the future.
Built the speed of draw just from practicing draw strokes over some time. Then, not being happy with the slower than I wanted progress of speed trying to concentrate on accuracy [ at least combat accuracy ], having discovered how twitch muscles are developed, I would run the gun out of control. I was only interested in trigger speed [ the training of the trigger finger to move faster for more shots per second ]. Isolating the training of the trigger finger, isolated the draw stroke and then the two came together when paired in a sequence of draw and fire practice.
I wouldn't recommend nor condone anyone that's a novice at handgun skills to instantly trying to shoot out of control to gain trigger speed anymore than I'd recommend or condone a new/novice shooter start yanking the gun out of the holster in an effort to be fast. Both would be unsafe for a novice, not well heeled in running a gun to begin with.
Lets say for the first 10 years, I advanced to a 6th grade level, after the boys showed me some real skills for the streets, lets say I went from 6th to 12th grade in the next year. And within two more years, I'd graduated college with a masters degree.
So, 10 years to get out of grade school, just 1 year to 12th and 2 more to a masters degree. There's a learning curve, but the more you have as a base, the faster you find can move through the grades till you're an accomplished SD pistol shooter with numerous skills behind you.