The only thing I would absolutely say they should not allow is copyright violation. Beyond that, it’s really up to the people that own the site. If a video does not fit the purpose they had in mind when creating it, then it should not be kept.
According to the about section of their website, “YouTube is the world’s most popular online video community, allowing millions of people to discover, watch and share originally-created videos. YouTube provides a forum for people to connect, inform, and inspire others across the globe and acts as a distribution platform for original content creators and advertisers large and small.” According to this description, anything that is not original to the person posting it does not really belong on the site.
So, within the “category” of original, I would say that they should allow everything. To be true to their purpose, they should not censor the types of material people include in their videos.
@HungryGuy How do you propose having people “prove” they are over 18?