While I agree the Adult trying to put their child to sleep on the floor is inappropriate, I have to put my 2 cents in.
I have on one occasion put my child on the floor to sleep at a Disney Restaurant. My 5 month old daughter fell asleep at Akershus. She does not sit up yet and they did not have room for a stroller for me to lay her in. It is not that easy or comfortable to eat with a baby in arm. We were tucked into a corner so I layered 2 blankets on the floor and put her down. She was not touching the floor as I do believe that would have been gross. I don't think of myself as trashy or irresponsible for doing this. Why would I leave a restaurant and ruin things for my whole family because my baby was tired (this was a 5pm dinner)? Yes, she was completely out of the way and no one even noticed her there because she was in a secluded corner. I also had my 4 yo son fall asleep while waiting for our O'hana dinner. (5:15 time I believe) We waited for an hour to be seated. By the time we were called, he crashed out on my lap. He slept on his chair with his head on my lap. Again, we were in a corner but even if not, I certainly would not have given up our reservation and left because he fell asleep. The rest of my family needed to eat and he wasn't hurting anyone by sleeping.
If my kids were being disruptive at any point I would have removed them but I can not see how anyone would expect you to leave a restaurant you planned months in advance, trekked over to and waited to eat at just because their child decided to take a snooze.
I may come under fire for this but it is hurtful to see people refer to this as inappropriate and trashy. I don't feel I did anything wrong in my situation. I enjoy Disney as much as the other person. We go every year and I am not always on
free dining so it didn't make me feel entitled.