The downside of solid, is when it has to be moved. Particularly if it is connecting a part that has to be lifted off for servicing. Solid wire will break after surprisingly few bends because the metal stress fatigues, especially on sharp bends.
Thanks couldn't have said it better
btw if you are worried about those stray wires just twist the strands to gather then solder them together that way they go in to the eyelets on the pots clean and easy