If you have a different case where a single attack class is potentially a problem I'm all ears. We should definitely be on the lookout for both balance and potential abuse.
Even before we get to balance or abuse, just IDK, symmetry? If the warlord essentially passes his turn to give someone a second turn, that turn should be a regular turn (for them), it shouldn't be a half-effectiveness turn for some and a double-effectiveness turn for others. It might be that a given character has a lot of attack potential every turn, so giving him an extra go is an obvious thing, but that's different from a mechanical artifact.
I guess it comes down to baseline at-will attacking scales at least three different ways in 5e. Cantrips, which scale damage
dice on a single attack roll (or save) with character level, Extra Attacks, which scale all sources of damage that apply to an attack with class level, and SA, scaling with Rogue level. OK, and there's EB which kinda scales more like Extra Attack than other cantrips. And, y'never know, something else could show up at any time.
So how do you make an attack-granting ability robust in the face of that?
I'm thinking: expend an action to grant an action, with a proviso that it can only be used "to attack" - and, if concerned about the balance issues of dissimilar level warlords & allies, limit the functional level of the granted action to the lower of the two (which seems too complicated for 5e - but
if you're that concerned about it, that'd be a way to rule).