Best exemplar of (self-) accompaniment on an instrument that springs to mind is Martin Carthy. Listening to his albums over the years, you can hear him refining the "less is more" approach.

I think he also nails the "instrumental break" very well. With Carthy's playing, the instrumental break is exactly that - a break, a respite, a much-needed pause for breath or reflection, with similar effect to the space on a page between the end of a chapter and the heading 'Chapter 2' in a novel.
I wouldn't say Martin Carthy plays "solos" exactly, he plays instrumental breaks, in the truest and most appropriate sense.