I think the main reason behind the "giving away a rabbit to a young girl" part falling out of favour is pretty simple, and actually explained by Penn in the act.
We care a lot more about animals and their treatment now, particularly looking after them, for which reason its incredibly rude to give a child a pet without at least having carefully arranged it beforehand with the parents - meaning a lot more setup work than in the past when pets were essentially disposable if things "didnt work out" looking after it.
As for the later part, Id be interested to hear more about the history of the sawn woman. I can find references to changing women's fashion making the routine more practical for a female assistant, and Id always have assumed the "loveliness" of the lovely assistant to play a part, but Ive never heard before about this other angle. Id love to know more about how it came about and how we know about it, but I cant find anything online in a quick search.