I thought the main reason the Remington Model 8 didn't make it to general issue was it's terrible stripping procedure, until I watched that BAR segment. What I find strange is that I have read extensively about the BAR and don't recall ever reading any complaints about takedown and reassembly.
David Hackworth wrote enthusiastically on the BAR service in Korea. I wonder how often a takedown of the order seen in the video was necessary.
This is a quick survey of a few books I have.
"Ordnance Went Up Front" by Roy F. Dunlap
"The Browning is a good gun, but it requires too much shop maintenance for use as a field weapon in all military branches. On a pro-rata basis, for more repair jobs were done on these automatic rifles than on any other weapon the US forces used, with the possible exception of the rocket launchers (bazookas). The BAR carbons up fast and th gas cylinder "body" or plug, which has the three differing sized gas ports for regulating the amount passed into the cylinder quickly sets and very often is impossible to remove without equiplment. When they cannot be cleaned often, they rust and when they rust they wear oversize and when they wear oversize they leak gas around the piston; the gun goes "bang," period, the next time it is tried. Back to the shop again, where the cylinder could be carefully clamped in a vise and a pipewrench applied to the plug. I preferred to heat expand the cylinder at the threads with a fast welding-torch treatment and unscrew them hot without marring the soft steel. The troopers usually could not remove them for cleaning every day the gun was used and a lot of them never seemed to learn that it was far more important to clean the gas handling parts than the barrel"
"US Infantry Weapons of the First World War" by Bruce N. Canfield
"Hatcher's Notebook" by Julian S. Hatcher.
"Use of Infantry Weapons in Korea" Operations Research Office, August 1952
"Of 22 officers questioned <snip>, five officers claimed that the BAR was too heavy and complicated, although not specifically asked."
"RELIABILITY - Statement: In winter 40 percent of them report no difficulty with the BAR functioning, but 38 percent say it is out of action one-fourth of the time or more (21 percent say one-half time or more). The corresponding figures for wet weather are 50 percent no difficulty, 22 percent out of action one-fourth of the time or more (10 percent one-half the tim). Of 17 officers commenting, 11 thought these percentages about right, Five thought the percentages out of action too high."
I also have a report on infantry weapons usage on Guadalcanal that Mike from BotR sent me a while back - it makes no mention of complexity or field stripping problems with the BAR.