I'm assuming they fly those plans routinely and just diverted for the day
Thats not really the whole of the argument here. You could literally dump the cash int he nurses lap and it would be more of a thank you to them than some plans flying over head.
That it is a shitty way to say thank you and not one that any one they were thanking either appreciated or wanted. From what I hear most of them would have rather them done nothing than to create a shit ton of pollution and waste a bunch of money for no reason.
If we're taking George-Washington-no-standing-army as a baseline (and that's a good baseline I can get behind) then yes, it's a waste of money. As it is, that flight and fuel was budgeted and spent long ago. Whether or not it's appreciated is up to the recipient but seems like a nice gesture to me
The idea that the money is pre-budgeted and couldnt be redirected is part of the problem I suppose, not so much a justification.
with that said there were probably much better gestures than that.