Horse archery is decent but requires retreating back to refill arrows, which feels pretty cheesy to me, otherwise the limited number of arrows you can carry evens it out for me.
I can kill far more on foot with a swinging polearm or long two hander than on horseback, bow or otherwise. Being so close to both enemy and allied troops makes it harder for ranged units to target you as well.
If I'm horseback with lance I can target Lords and high value targets and one-shot them, something that's far harder on foot, which I feel is pretty fairly balanced with the increased risk from velocity bonus and being more exposed in general.
Haven't played Native for a long time though, so maybe looters are death machines there. Games terrible without mods anyway, plenty I use solve that problem pretty easily, so I'd just recommend use mods and give up on TW changing these things.