My father used to do that with me. But we where in the middle of a 3 acre flat lawn with 3 trees in it. I know I won't ever be doing that when I have kids.
I have been with several of these types of calls with the fire department. Some people are just stupid.
Here in Maryland, nothing is flat. So why would you add the extra weight of a kid, plus their weight is also not being balanced over the center of the machine.
I did see a john deere garden tractor once with a smaller seat attached to the bigger seat with a little seat belt on it.