I haven't found a problem with sites and players not wanting to write fandoms in general. They're everywhere. It is difficult, however, if you, like me, are into a niche tv show or a specific pairing only and not many people know about it. The pool is tiny and you may not find a suitable player in it anyway.
That said, I would write in a fandom. But I usually don't because 1) I don't care for 99.9% of the tv shows, books, movies etc I consume or, more pertinent to your question, the characters in them and 2) I refuse to do canon x OC because primarily, I assume that the OC will be a Mary Sue and secondarily, I've already shipped the canon character I would play with another canon character to leave no room for anyone else.
I've got a couple of fandom pairings I am looking for in my interest check. I would play these characters because I love them and it's fun to explore their back stories, consider and write out their reactions to future created events. I love being in their world and to have adventures with them. These are characters I would or have spent a lot of time thinking about their personalities, their whys and wherefores, their POV in various aspects; all grounded by (somewhat) relevant canon justifications, by my trying to stay as true to the source material as I can. As such, I feel icky to use my babies and romance some Mary Sue. And when I am partnering up with somebody else who's playing the counterpart of our specific pairing, we would exchange fanfics or writing samples first to see if our versions of the characters are to our tastes. A last trivial reason would be that I find it requires much more brain power and tiring to consistently stay in-character as compared to writing for OCs. I analyse everything every time I post again and again to make sure the dialogue, action, body language, etc, are all (kind of) acceptable; while it's a breeze to take on OCs because they're mine and I can mould them however I want.
So, for me, I wander out in original worlds because my fandom parameters are stringent.