Making movement speed, if even possible, based on the amount of AG would make AP too much more important than it already is in battle.
That's silly. You are OK with it being in TB, yet it feels wrong in RT?
Look HP is important as well, so is your sight range. There are some stats that bring little to nothing though. Like there is almost no benefit from having more strength than your weapon requires. Same for intelligence as well.
Also remember when all the values are not that important, customization is usually just boring and game as well.
Imagine action points being as irrelevant as carry weight for example. That's how it works in F3. All your stats are just boring numbers instead of actually defining your character.
I buy the animation issues, maybe even other issues as network stability, but that's something that can be resolved for example by making current speed the highest speed possible to achieve (well probably not just like that, because everyone would move way too slow, but you get the idea). To be honest in Fallout your character run goddamn fast and it did not look that bad.