I think the discussion is going into the wrong direction, because it turns to yet nother OP/UP-discussion about HAs.
First things first: I hate HAs. I hate them so much. Not only do they attack over safe distance like archers, which is lame enough, they also have a horse under their arse, making them run away really fast as soon as they encounter any danger. Lame.
But why is it lame? Because I am infantry, and my objective is to kill the entire enemy team. Now good luck with killing horse archers. I don't think many people have a problem with how much damage HAs deal, they have a problem with how difficult they are to kill (while being able to attack you all the time!).
And I think there is nothing you can ever do about it. That's how things were back then, in history, which was real, and which was not about creating a fair game. It was about finding the most effective weapon and to have the biggest advantage possible over the enemy. And horse archery was that ultimate weapon for quite a long time. So game-balance wise there is absolutely nothing you can do about. If horse archers would NOT be able to attack over range, or would NOT have superior mobility, allowing them to escape of dangerous situations, they wouldn't be horse archers any more, and the class wouldn't work any more.
Their effectivity has been lowered a lot in the last few patches, anyway. I'd dare to say that together with archers and cavalry (especially heavy cav) they are the most UP classes in the game. Yes, on one hand it seems weird to say that the classes people tend to complain about most are the most UP classes, but on the other hand it is very logical: there is something wrong with the MECHANICS of those classes, and the devs tried to fix it with lowering the EFFECTIVITY.
The only solution which I can come up with, is a different game mode. Because it's the only way to influence the mechanics without changing them. The classes must still be able to do what they are meant to do, but the use for winning the round needs to be shifted. Of course a horse archer is the perfect symbiosis of dealing damage to whoever they want whenever they want and one of the highest survivabilities in the whole game, which is literally the optimal class for a game mode which has the goal of killing the enemy and surviving yourself.
But how much would this help you if you'd have to stay next to a flag some time? And the flag is perhaps even in "difficult" terrain? (Ruins, woods, rocks, hills, villages, fortifications, castles, water) Suddenly you wouldn't be that effective any more. Your survivability would'nt be that important any more, because killing you is not the objective any more. And you killing all the enemies wouldn't be so much of a problem, any more, because if the last hand full of players manages to fend off the surviving majority of the enemy team for a certain time, they will win the round. Which is definitey a better condition that having to kill every enemy.
Perhaps there are other solutions out there, but I spent lot of time thinking about the problem, and this is the only idea I had. The only one which keeps the mechanics AND the effectivity untouched, but solves the problem. If you find some other idea, which...
... does not include effectivity nerfs (speed, damage, upkeep, etc.)
... does not change mechanics (e.g. making HA's unable to shoot while moving)
... does not change the game mode (we already had that idea)
.. then tell us.
P.S.: just a small addition: class restrictions shouldn't be the way to go, either. I think it's a horrible solution for a game which is about developing your personal favourite build, you shouldn't be restricted in that freedom.