For me, "improving speed" is a whole distinct category of practice.
First, I'm not going to work on improving speed for speed's sake on a skill I cannot perform repeatably 100% at a calm pace.
Once I have the skill down enough to do it right every time when I'm not worried about speed, I can begin to spend some of my practice time on building the speed. Personally, I usually use 90% as my target when pushing for speed. If I'm missing more than that over the course of many multiple reps, I'm getting ahead of myself.
Under some circumstances, it can be worthwhile to push yourself to maximum speed, damn the results, just to find how fast you can move & see. My biggest problem with this is that many people turn this into their normal practice method (even if they don't realize it) and those are the folks who have the hardest time dialing back when they need to be 100%. Years ago, there was a period of time when SLG and I stopped worrying about 100% on low% targets and spent a lot of practice on hitting a giant 8.5x11 sheet of paper at 5yd as many times as we could in a given PAR. That taught me a lot about seeing faster, tracking my sights faster, etc. But it's not something I do every time I go to the range or even every month.
Like I said in my first post, a lot of this comes down to what your goals are. For some folks, "be faster" is the goal. And that's a perfectly reasonable goal. But for other folks, "be more consistent" is a goal and it's equally as reasonable. In my experience, the latter approach is a better method for building 1-time on-demand cold performance. At a match, I can walk over to the safe area and warm up my draw, reloads, sights & trigger, etc. I'm going to shoot four, ten, twenty stages and know that not every shot on every stage is going to be perfect. But if I'm out to dinner with my wife and someone decides to go all SpreeKill on us, or I'm in the parking lot and someone tries to mug me, there won't be a warm up and there won't be a chance for reshoots or makeups.
edited to add: GJM, I find this line of questioning interesting given your response to the 3x5 Speed Push DotW awhile back.