No, I wouldn't allow sneak attack on a reaction. A reaction is not a "turn". I rule that rogues get their sneak attack on their turn, just like every other class gets their bonus damage on their turn. But, again, that's not the point. You claimed that a rogue with several warlords granting him actions would be broken. But, Battlemasters already do that right now. A rogue with three battlmasters could get 4 sneak attacks per round. If that's not broken or a problem, why would it be a problem for a rogue with three warlords granting him actions?
By and large, yup, I'd see that as a limited resource. Perhaps not as limited as a Battlemaster - spending Superiority dice and losing an attack to grant someone an attack is pretty limited. An 8th level battle master could, at best, grant 5 attacks per short rest. I presume 10 rounds of combat between rests as a baseline (2-3 combats seems about right), so, at best, the BM is granting an extra attack every other round. And that's the limit of what he could do. He couldn't also grant bonus movement or heal. That's not enough to make a warlord. If I could grant a bonus attack every other round AND a bonus movement every other round AND grant some healing (in whatever form) that would be a warlord.
It's not enough to be a warlord if you're only actually a warlord half the time and the other half, you are a poor man's fighter (since you blew all your Sup Dice on granting actions, you can't do anything else - you're not even as good of a fighter as the Champion at that point).
For it to be an at will thing, you'd have to spend an Action - as in no attacks for you. That would likely balance out fairly well.
Then again, the simplest solution to things like Smite and Sneak Attack is for granted actions to occur on allies turns. So, I give up my action on my turn and on your turn, you gain some sort of action - bonus single attack, bonus movement, something like that. No different than how buffing magic works.