Admin Forum:Should I delete conversations on a Talk page?

There seems to be an argument that has sprung up on my mid-size wiki: Is a Talk page just for talking about ways to improve the page alone, or can it be used to argue about the content of a page? For example, if it's a page about a movie, is it inappropriate for a user to start a debate about how the movie is better than the television show it is based on?

And as an admin, is it appropriate for me to delete such nonproductive banter? --BlazingStar (My talk) 00:43, November 2, 2012 (UTC)