My singing days are long past, not enough breath anymore, however, thirty or so years ago I used to try to sing a varied repertoire of traditional, modern and rubbish that I had written myself. The problem was, I had performed a few songs which people could not forget, so when I got up, someone would always say 'Sing The Dinghy',or 'Johnny'.
In the end, it becomes a kind of flattery, you do it to please them, but it pleases you to be asked.
I do see where breezy is coming from though, there are still performers like the old guy in 'Lark Rise' who always sang 'The Outlandish Knight'.... Badly!