I also have the same issue with no mods in the game. I assumed it was just the way the object was made, but I agree that it seems pretty stupid. It's extremely unnatural to put your baby on the floor after giving them a bath. Kinda counterproductive.
I know I am super SUPER late and you've probably already found a solution, but there is a mod so that sims don't put their babies down after changing them. I just found it, and it works wonders! http://www.simlogical.com/ContentUploadsRemote/uploads/2192/
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Does the monitor still cancel all the parent's interractions?
Send me a friend request for Simport