If I recall correctly, (it's been a long time since I've done PAM drills) The bolt catch IS part of the reload drills. So that's what is taught in basic. "Strike the Bolt Release" I believe is the phrase that's used.
the Current CF Gunfighter package is great; I believe all soldiers who leave the wire are required to undergo a certain amount of Gunfighter training. I know passing the PWT 4 (instinctive shooting) was the requisite for us and our attachments. (Battlegroup tour) I don't believe as a whole we practice shooting enough, but that's a whole other topic.
The biggest constraint on "speed reloads" and such is that often in those videos you see their kit is optimized in some way to make the reload easier (often not having the magazines fully seated in the pouches) so that in real life, reloads become a much more drawn out affair. I can approach the times that buddy in that video could with the reload, but when I load my rig up with 10 Magazines, 12+ 40mm rounds, 5L of water, IFAK, TCCC, NVGs, Pistol...(that was what I carried overseas) stuff begins to get harder to take out. Reloading is something we do from cover. Always. As soon as my bolt locks to the rear my reaction is to drop. I rely on buddy on my left and right to keep an eye on the baddie while I throw a new mag in.
One last point, ref using the bolt catch versus the charging handle; when you get stressed to the level of being in the Orange/Red (such as in combat) your fine motor skills are greatly reduced. As a result, hitting that bolt catch can actually be really difficult. What we do is make it so that using the cocking handle at all times is pure muscle memory. The time it adds to the reload is NEGLIGIBLE. You do it in the same motion as seating the new mag.