"We've got books full of songs. It's just not practical to learn every one of them, ..."

Why not? It is said, 'Girl Friday', that Henry Burstow knew 400 songs and could sing them, one after the other, over several days (without notes).

I probably know about 50 (I'm no Henry Burstow!), including a few 20 verse ballads. I know them all by heart and never use a crib sheet. I don't find learning songs particularly easy - but who said singing should be easy? If you care enough about the songs and your audience you'll put the effort in.