The modernization effort for the M1/2/3 Carbine as a result of Korea eventually resulted in the AR-15/M-16:
https://www.thefirearmblog.com/blog/2014/07/08/weekly-dtic-hitchman-gustafson-reports/
This has been tested with M1 Carbines since and found that a refurbished Carbine with regular ammo had no problem penetrating targets mocked up to mimic the clothing of the Chinese in winter at greater ranges than reported in Korea. I can even post some videos of some tests if you want.
Likely the problem was people panicking and missing in combat and the use of older ammo. A lot of WW2 stocks were defective after being kept in improper storage or not being refurbished properly, which was not limited to M1 Carbines. Likely the extreme cold coupled with the improper storage and degradation of the ammo and or carbines themselves resulted in weak performance of the ammo compared to spec and then it either couldn't penetrate the clothing or missed altogether. Per SLA Marshall's report there were some units that had no problems with the Carbine and like it quite a bit; likely they either got new issue weapon/ammo or whatever the best stored equipment/ammo was.
BARs were preferred because automatic fire gave everyone confidence, plus you don't need to aim precisely, which is what the reports said soldiers were not doing with their M1. They were laying down suppressive fire quickly rather than aiming in most cases; it was even stated that a lot of M1 sights broke or were defective, so soldiers often couldn't really aim. The BAR due to the cone of fire it produced allowed it to achieve hits at range without precise aiming. Point it in the general direction of the enemy and you're more likely to achieve hits with a burst of fire. It was basically the basis of Project SALVO, which was predicated on OR from Korea that showed soldiers aiming errors meant that even the most accurate weapon was effectively pointless and something that produced a burst of projectiles with low recoil got you the best chance to achieve a hit. Hence the SPIW with it's multiple flechette rounds and the duplex ammo as a backup.