Of all the basses I’ve had the ones that have moved most have been 3 of my Seis. All were laminates and the one that moved most had carbon fibre rods too. I had a Status with a twisted carbon fibre neck once.
My Rics, however, once set, have hardly moved at all. My favourite-sounding bass, my Feb ‘72 4001, has a one piece neck, which was once described by John Diggins as “spongey”, and yet it sounds wonderful IMO. I think both sound and stability depend on the individual instrument.