A couple of people have commented on the limitations to improvising around the tune in sessions, and I'm not sure it's quite as limited as implied. I've had the pleasure of attending some pub sessions in the past with a core of sensitive, accomplished musicians who were able to follow each other into a whole world of chordal and rhythmic improvisation, and always come back to the 'original' tune - so it can't have been too far lost.

I agree that it's really difficult to do, and that it's probably easier with simple English tunes than with complex Irish melodies (for example), but it does happen, and it's magical when it does.