You can't expect to have good accuracy and be able to take down medium-heavy targets as a HA. One or the other, Power Draw or accuracy.
Skirmish, shoot soft targets, harass archers, gun down unarmoured horses, provide helpful knockdown bumps, distract lancers. I've done HA for many gens as well, sounds like you need to learn the limitations and/or change your expectations. Winning isn't just about getting kills.
That said, something does need to be done about the HA-HX imbalance, where HX hold every advantage, but that's a whole different topic.