I was practicing this morning and happened on a very simple bass riff, basically a single repeated note, and thought that’s familiar. It’s was the bass line to the Simple Minds song, Waterfront.
Many songs by Social Distortion. To start, try Cold Feelings. In fact, this is me, on my previous BB734A that I owned before my current one, waiting for my bandmate to cover the guitar part
The Carpenters version was a cover itself, of a song by Delaney and Bonnie and Friends called Groupie (Superstar). The and Friends included Duane Allman, Leon Russell, Rita Coolidge, and Eric Clapton. The song is about an encounter between Coolidge and Clapton, both of whom performed on the original recording.
There’s an Eminem song (Lose Yourself?) that is simply low D eigth notes - the entire song. IMO it’s actually challenging to play something that monotonous well for the whole song…
And I’m sure that there a whole lot of examples of playing root notes that follow the chord changes (Ramones comes to mind) - while its not “1 note”, it’s “1 note/chord”…