The pub may be a public space but the session is the collective property of the people who play/sing in it. Its up to them to make the rules.
I suggest it would work far better if everyone recognised that they were, and all acted like guests (not, I would add in The Mudcat sense of that word). And that the sessions were taking place on premises were neutral territory and not ours to defend.
The music being made does not belong to anyone but everyone and the only rule that is really required and will always work is - if what is happening (or not happening), is not to your liking, then YOU leave and find, or start something that is.