Your main point is a good idea. I'd like that too.
Just want to throw in though, "1H on horseback useless" isn't necessarily true. The big distinction between 1H & 2H is damage and whether or not a shield can be equipped. Which was true in Warband as well. But in WB 2H weapons were also longer...that length/reach distinction hasn't entirely disappeared, but is a lot more blurred in Bannerlord. There are some 1H weapons that are just as long as many 2H weapons. "The Ambassador" (common tourney prize 1H sword at 114 length) is one example. "Cavalry Broadsword" (117 length) is another. They work from horseback just fine.
I'd agree that most 1H weapons, especially lower tier ones, yeah, too short for optimal mounted use. Just wanted to mention there's some reasonably accessible exceptions.