My primary shooting partner and I warm up with that nearly ever day we shoot. The org he trains security staff for overseas has a much more generous standard than that but I work for under 3 sec, and sometimes press for under 2.5 that you mentioned. 100% in the target you described in 2.5 sec or less is a standard I have not achieved. That's pretty strong.
GJM - I'm tracking . . . for the most part. I don't think slow concentrated precision is deleterious for it's "loading the program" (Proctor phrase) with the deliberate feedback one can absorb from it. But I wouldn't make it the majority of my time spent.
Reading this before I headed out to shoot this AM I used my timer for the 10 shots I fired at 25 yards with my G17 this am. Other than shooting the draw and fire a single referenced above, I can't remember ever putting a timer on my 25 yard "group" shooting. Interesting.
https://www.flickr.com/photos/78036189@N07/14981411759/
edit The shoot on command drill that Wayne mentioned is very cool.