I'm not sure what you mean by the "Cove and New Star" sessions, or why you think they don't need the small events exemption.

My understanding is that all live music is Regulated Entertainment, however spontaneous performances by the customers themselves are exempted. Since most folk sessions either take place on a regular basis, or require a degree of organisation, they are not "spontaneous". Or am I missing something?

The small events exemption will remove most sessions from being Regulated Entertainment. However, unless the "entertainment facility" rule is changed, the venue would still need a licence for a piano (even if it isn't played) but not for the music, which even the Government seems to recognise is nonsense.