Yeah, the full cast Stargates have a lot of "Well, Cam and Sam are busy... elsewhere... with things." (Though that they couldn't do a full field team is a little disappointing-- BF does have four-member TARDIS teams sometimes.)The Doctor Who ones work well because you only have a cast of 2-3 regulars to accommodate, plus guest stars. A Star Trek show would have to pare down the cast significantly, which would result in a very different kind of story than we're used to. (Even the Stargate audios couldn't manage to include a complete team of four.)
I think of all the televison shows, DS9 would work best on audio-- it's got the set-up where it's the easiest for not all characters to have to be doing the same thing at the same time, since they don't all hang out on the bridge together all day long.