This is getting more ridiculous by the minute. It is not a favor to get paid. I am not doing my employer a favor by showing up to work. If you don’t take payment and it is a favor, then it should be done as such and not begrudgingly. If I ask you last minute probably it is because what childcare I had arranged fell through. I don’t expect it will be easy to find a sitter last minute but I am not going to not try just because my original plans didn’t work out.
However I do agree with the food/ drink part and always try to mention a few specific things I have they can take along with “feel free to take anything you want.” I say this even to my niece who knows where everything is just so she knows if she gets hungry she can feel free to find sonmething. I also try to leave money if it’s during dinner time that they can order pizza to be delivered.
But if I don’t offer food or do call last minute, that doesn’t mean I “can’t handle” a babysitter. As pointed out, if you don’t want to take the job, say no.