I've been pondering this, as shopping questions tend to be thrown out across the whole of SE. Still, it'd be a useful question to ask sometimes for some people, with potentially singular answers.
Can they be asked, and should they be?
No, as these are a form of game recommendation question and these are generally not accepted on this site. There is a long, complex and contentious history behind the eventual decision to disallow this type of question, and there is still some ill-feeling about the way it was handled. However, the decision to ban them still stands.
If you're interested, do a search for the [game-recommendation] tag on meta to get the whole story.
Yes. They are distinct from shopping questions, so long as X is specific enough (e.g. x = "Star Trek" is fine, x = "comics" is not).
If it helps to think of it differently, "how many RPGs have been based on X?" asks the same question in a different way, and is much more clearly not a shopping question.