http://www.thestar.co.uk/headlines/West-Street-dubbed-neighbourhood-from.6587837.jp

John King comments:
What has all this urinating and fighting got to do with live music?

Nothing of course, but invariably local authorities allow extended opening hours with permission for recorded music while banning live music.
...
So a DJ is allowed where an unamplified piano is illegal.

The application itself already limits the entertainment. The licensee could and should be able to decide for themselves, the time that various activities cease, there is no need to have entertainment ending a full hour before closing time as a licensing condition.

But again and again we see one licensable activity (live music) being limited and used in order to enable another (serving alcohol).

The activity which is being limited, is the one with many benefits and the one being encouraged, is the one presenting the problems. How did this crazy situation happen?

The Licensing Act 2003 list all the licensable activies - it does not require Licensing Authorities to limit and use one to enable another. As the Act does not state which licensable activity should take priority over another - the reasonable assumption is that they should be treated equally.