It should not be the visitors' job to ask that this should not happen, but the other way round - if they have no objection they can say so, otherwise they have a right to be listened to in silence.

It is pretty obvious which kind of tunes work best as an accompanied solo (or with a tightly thought-out accompaniment by only one player) - if Paul Anderson started up "Gight Castle" in a Scottish session it is not likely anyone would play along. He wouldn't NEED to say when silence was a good idea, the tune and the performer's attitude will convey it in the first bar. Nor should I need to say when silence is a bad idea to the point of being downright insulting, but I guess people who sing Neil Young are just thick.

You might need an explicit sign on the wall to say what to do, but the non-autistic majority of us are well able to read the social and musical interactions in a session situation.

I can go to a ballad performance of the type you describe every week in Edinburgh (though I haven't, Fridays are not convenient for me) - Kevin Mitchell (note spelling) has sung at it, I think. Nobody would go along to that with the idea of accompanying anybody, but I doubt they've ever bothered making a rule about it. There's a session upstairs in the same pub at the same time which operates under something more like the usual session conventions. The people who go to that don't need to be told what to do, either.