The point is it's not up to the publican.

Or rather it is, but the law means that the publican who lets you sing or make live music is taking a risk. Noone is disputing the right of a publican to stop people making music. But the law interferes with the publican's right to allow people to make music.

Or indeed the right of anyone managing any place to which the public have access to allow people to make music or sing.