I have been introduced to trad songs/tunes through the clubs I've attended, and I probably wouldn't have attended them if they were "policy" traditional only clubs or sessions.

Are there any trad-only clubs or sessions? I don't think I've ever been to one.

There are quite a few no-trad-allowed clubs and sessions, as the Sandbach example shows (and as is the situation in practice with some of the sessions in Midlothian, and at virtually any event anywhere described as an "open mike"). But the other way round? Really?