Richard.

Public = public can get in.
Entertainment = to be gawped at or possibly but not necessarily participated in or enjoyed.

2 public entertainers = no licence needed. Are 2 darts or pool players in a pub team on a match night with an audience, public entertainers?…. By your definition. Yes.

Does a pub have to hold a public entertainment licence?….By your definition. No.

3 public entertainers = licence needed. Are 3 darts or pool players in a pub team on a match night, with an audience, public entertainers?…. By your definition. Yes.

Does the pub have to hold a Public Entertainment Licence? ….Again by your definition, Yes.

No one (even you) it would appear, is really claiming to that the need for a PEL is being interpreted as applying to 3 darts or pool players, providing largely their own entertainment.

Then it surely must follow that it cannot apply to 3 musicians, providing largely their own entertainment, with the publican's permission of course.