If I had power over it.

I would indeed make the mentor only version require that there be a first timer in there.

On the other hand, I'd make an almost exactly the same one, open for anybody who meets certain, magical, ever changing (people will figure it out in hours) requirements, but is otherwise completely public and does not require mentorship, that cleans up any que that's gone longer then 15 minutes, no matter WHAT it is.