Perhaps there is a generational/geographical gap between us. When I was growing up, we played with friends in our neighborhood. If we wanted to go in someone's house, we'd ask mom. There was no "dropping off" b/c there was no driving. It was someone right down the street and the moms all knew each other. Otherwise we were all just hanging around outside or in the woods/fields, etc.
So for me, it's a very odd concept for someone to drive over to my house to drop off their child and leave.
I'm also pretty horrified that you think a mother who wants some "me time" is somehow bad or defective. I'm sure you didn't mean that as horribly offensive and ridiculous as it came out. Particularly since you completely contradict yourself, saying that as a child you and all the kids ran around the neighborhood (presumably leaving your mothers alone), while implying that a mother who is separated from her child nowadays for so much as a boy scout meeting may as well be ditching her kid to run off to Borneo to find herself. Surveys show that parents, even parents who work full time jobs, spend more time with their kids than ever before.