Maybe it's because sitcoms aren't as plot- and characterdriven as drama series? I mean, on a drama series you tend to have plotarchs and character development, whereas with sitcoms you often have a status quo. And yeah, having to be funny is always quite daunting.

Although there's one sitcom I know of, The Big Bang Theory, which DOES get a lot of fanfic and has passionate shippers. But then something as massively popular as Friends, for example, I think that's fairly small fandom- and fanficwise.