Let hypothetically say that there was a summoned creature (let call him "Jack")out there with a basic attack so we can broach the original question.
Most of the time action economy dictates that the summoner must use an action for the summoned creature to act. The concept is that you can bring more creatures onto the field, but you cant bring more action. For the creature to act, someone has to pay a price from their own action budget.
Following that, if we had said that a warlord uses commanders strike to allow Jack to make his basic attack, I as a DM would have absolutely no problem with this what-so-ever, because it is consistent with the concept of the action budget. In this case the warlord has used some of his budget instead of the original summoner, but a price has been paid.
My take, as long as a creature has a basic attack, I would pay it
Most of the time action economy dictates that the summoner must use an action for the summoned creature to act. The concept is that you can bring more creatures onto the field, but you cant bring more action. For the creature to act, someone has to pay a price from their own action budget.
Following that, if we had said that a warlord uses commanders strike to allow Jack to make his basic attack, I as a DM would have absolutely no problem with this what-so-ever, because it is consistent with the concept of the action budget. In this case the warlord has used some of his budget instead of the original summoner, but a price has been paid.
My take, as long as a creature has a basic attack, I would pay it