It's up to the FM or TV station to decide whether it wants the call with the suffix or not. Unless the un-suffixed call is already in use elsewhere, in which case you have to take the suffix.But not all FMs have the "-FM" suffix, right? Just the ones that have AMs -- or TVs -- with the same call letters? And what happens when the owner of such an FM decides to change its call for imaging purposes? Would, say, WNEW-FM become just WZZZ, not WZZZ-FM, under those circumstances? (Just a made-up hypothetical call, BTW. I'm not going to search a database for available letter combinations just to make this post 100 percent accurate.)
Case study: the public TV station in Rochester went on in 1966 as simply WXXI, no suffix. In 1974 it added an FM station as WXXI-FM. And then in 1984 it bought an AM station. In order to put "WXXI" on the AM station (no suffix), the TV had to become WXXI-TV.