I’m not sure how “here are things you can do with movement, many of which change your position and possibly that of one or more other creatures” will suppress movement.
If you disincentivize moving (with AoO), and give incentive to do something else with movement (cool footwork), the likely/expected result is folks not actually moving much.
If "have people stand still and deliver" is a goal, then fine.
As for OAs already doing so, I’ll just say that is very much not my experience. Generally, it is very easy to circumvent them.
In what ways do you have people circumventing them?
I don’t think this necessarily follows. Steady Aim is more costly than its benefit merits, to begin with. I don’t have to give up any of my movement to Hide for advantage.
Steady Aim uses a bonus action and all your movement, and automatically grants advantage.
Hide (for a rogue with Cunning Action) takes a Bonus action for a Stealth check, which can either be impossible or fail, to do the same thing. Either that, or the Hide takes your Action for the round, which is even more expensive.
Hide is cheaper, but less certain and more situational. That seems fair.