I was also worried that mounted archery would be too simple. Fortunately the awkwardness of the controls makes aiming a sometimes frustrating experience

Nah, it's not
that bad. The thing to remember is, you only have a 180-degree arc of fire to work with. And really, you only have an
effective 90-degree arc, from roughly 10 to 2 o'clock in front of you. That's because when you are aiming totally to the left or totally to the right, your ability to turn is limited to one direction only. Also, when aiming at 9 or 3 o'clock like that, the crosshair doesn't seem to always really represent where the arrow is going.
It all boils down to the fact that you need to be facing the direction of your enemy at least somewhat to get a good chance of hitting. If you're moving while shooting, that means you need to essentially be riding
toward your enemy. If they are a fast melee NPC or creature, you'll be able to get off maybe a couple of shots before you need to break off, gallop away, turn and repeat. (This is exactly why fighting wolves and bears can be really irritating if you miss that first shot - it's basically impossible to get distance from them and they will nip at your horse's heels while you spin around in a silly circle trying to line up a shot.)
So yeah, if we had a Parthian shot kind of mechanic where you could fire in 360 degrees around you, mounted archery might be OP. But we don't... yet. (As a side note, it might be cool to have some extra branches in the Archery tree that would allow for this kind of difficult maneuver... and similar 'mounted combat' perks for 1-handed, 2-handed, etc.)
Currently, mounted archery is great for fighting giants and mammoths. They are big, so they're easy to hit, but also fast, so the horse allows you to run circles and figure-eights around them. It's actually a lot of fun.