All the same, Nick, I have received monies from MCPS/PRS for recordings of my songs. It's based on how many copies of the albums were manufactured. There's also the issue of monies if and when the recordings are played on the radio (let's not discuss streaming services, to keep my language clean) and if and when the songs are played live on any suitably licensed stage. Or of course used in any soundtrack for film/video/game etc. The performer doesn't have to pay these, but the songwriter or songwriter's estate loses out if the songs aren't correctly attributed.
It's not a fortune, as my accounts demonstrate, but the point is that you can't assume that a deceased songwriter's songs are free for anyone to take over.
Yes, I too have had performers (particularly from the US) give me cheques for their calculation of their liability for recording my songs. Never had any squeals from the middlemen because the middlemen never had to hear about it. Not going to happen these days because I've got a publisher instead of doing it all myself.