"the leader was turning the pages of his wee book saying we'll do number 22 and then 41"

As I said, every session is different and there's a place for everything. What you have described is either a beginner's session or a group of musicians who may have attended the same course or whatever.
There are some like that in Edinburgh and why not?

Even in Sandy Bell's, I think they used to (maybe still do)have an Intermediate "Moothie Session" and a slower fiddle session on alternate Mondays in the early evening but most of the sessions aren't like that.

Barbara was mainly reminiscing about the old days. Basically, she was saying that it wasn't really a music pub as such but sometimes it "happened". However, in those days, it wasn't presumed that one had the *right* to sing or play.
Nowadays, it IS advertised as a music pub with mostly organised sessions. Of course, this won't suit everyone but it is what is.

Back in the day, the customers in old Forest Hill bar were quite varied. There were the "auld worthies/crusties, writers, poets, university students and lecturers, medics (Inspiration for the famous Sandy Bell's man song) and, yes, a few folkie types at the back.

Times have changed and we need to accept this, Barbara included.
As I say, there's actually something for everyone in Edinburgh these days if you know where to look.