I tried to post yesterday but for some reason it hasn't appeared. I'll try again:

The dance school (which was the original subject of this thread) is one thing - as Mark says, it is a commercial concern and should be prepared to pay for all the resources it uses, including the music.

The situation with sessions is a bit different. In most cases, in my experience, these are not run by the pub landlord to promote his business, but by the customers for their own enjoyment. No one is making money out of the performance, and the landlord may or may not make extra money out of it from bar sales. In a number of cases, the the Three Stags' Heads being only the latest, the landlord has presumably taken the view that any additional bar sales are not sufficient to cover the extra cost of a PRS licence. This suggests to me that PRS has got its fee scales wrong for this type of performance.