As I've come across references to training 'point' shooting, the preference generally seems to have been to teach fundemental positions and aiming first. However there was at least one study (At Ft Hood IIRC) where the platoon taught point shooting first, overall did better. This was during WW2 as they developed combat training for infantry, tank destroyers and other MOS most likely to see small arms combat. They also had to train as many men as possible in the facility avialable, so they wanted to see if they could run both phases at the same time and then switch. The USMC also had 'familiarization' courses which were short, somewhat low round count, and more close combat oriented. However these all were in addition to and following rifle qualification. Of course in a military context rifles are the main weapon, and being able to estimate range, make adjustments and hit targets out to 500 yards is pretty important.
After WW2, the idea of some sort of combat point shooting did not disappear. Trainfire shows up in the 1950s and continued in various versions.
I'm aware of one well recognized trainer today who has advocated for point shooting with novices first. There may be more nuance to that -and Sublime One has taken and passed his instructor courses so I'm sure he knows a lot more about it than I.
I personally use sights (when available) because (a) that's how I was taught (b) with sights I can self-coach to some degree.
