Forget any linkage between baggage delivery times and carry-on policy.
Plain and simple, on a standard configuration domestic single aisle aircraft, there is not enough OH space to accommodate one compliant bag per passenger in the OH. Some people don't have such a bag, some people have a smaller one, and others don't have a second bag. But, with full aircraft there are still few flights where all bags can be boarded.
At the same time, the same aircraft which can be boarded for an intra-European flight in 10-15 minutes takes 20-25 at best in the US. It isn't just the GA's, it's that passengers don't listen and some of the worst offenders are the high-level elites and F pax who likely do know exactly what they are doing.