It seems to me, though, that most American Pop/Country/Folk singers affect soft r's, whether to imitate southern Af-American accent (so 'go' can rhyme with 'door', for example), or to avoid the 'harsh' sound of the hard r, as 'trained' singers do.

I do agree that the mimicry is not 'deliberate' - in the sense that it's not thought-out. For most singers, it apparently goes without saying - or thinking - that you want to mimic what you're hearing, if you like it - in the same way that so many guitarists will try to imitate what's on a recording, and judge their own performance by how closely it corresponds to what's on the recording - as opposed to, for example, doing it their own way.