"I suspect one reason may be that the repertoire is expanding faster than they can cope with; ....... In a situation where they were just playing to mostly non-musical social and family circle, as might have been the case a few decades ago, there was less pressure to know lots of stuff."

I've not quoted Jack's entire paragraph but there's a lot of truth in this. There does seem to be many more songs and tunes these days or, at least, the availability and access is much easier.

I too have lots of tunes where I still "rely on the paper". For many of these, this is just a transient process and I will eventually know them well enough to play in public either "off by heart" or to be able to join in if someone else starts them.
Some, of course, I may never get around to learning properly for various reasons but surely these are the ones which can be safely "left out" in a public situation?

Occasionally, I may bring in a song or tune sheet for a particular item which I may wish to perform as it's topical or something I've just recently learned(The music is a safety net but I hopefully don't need to look)but I certainly wouldn't bring in sheet music as a matter of course.