Lots of stuff to unravel here.
First, one does not compare a classical musician to a painter or other visual artist, simply because they are at different points in the creativity process. The painter is more like the composer playing his own works--both the idea and the execution are part of the visual artist's expression.
A great musician playing music composed by someone else must connect to the composer's idea, and then add their own ideas on top of that. The instructions for reproduction are, in that sense, a guideline rather than a rule. I have been told by teachers that a skilled musician plays the correct pitch, at the correct time, at the correct loudness, and with the correct articulation. That's the starting point of good performance--a good musician starts as a skilled musician and goes on from there. The musician playing from written music is an interpreter more than a creator, like an actor. Both work from an inner voice--the perfect representation of the art as they interpret it.
Musicians find the instrument that allows them to express their inner voice most fluidly and with the least effort. Part of that is how the instrument feels in their hands, even when that feel has no objective effect on the sound produced. Tuba players like instruments that vibrate in their hands, even though such vibration does not affect the sound produced in any material way. For them, the instrument feels alive. The best tuba players don't need that, actually--they are laser-focused on the sound and product that reaches the audience. I think what makes them world-class performers, and not merely highly skilled, is how well they connect what they are doing to what the audience is perceiving, and not just what they perceive as performers, using all their senses. But I certainly appreciate the feel of a fine tuba even if the product I put out there is kind of sucky. That said, different instruments have different sounds, and that's why most tuba players have several instruments, so that they can tailor their sound to the situation.
Violins: I know a violin maker of high repute. He studied in Cremona, is fluent in Italian, and has been allowed to make very detailed measurements of real Strads, Guarneris, and Amatis. I don't just mean external measurements--he also measured the thickness of the parts at many places for instruments that had been disassembled during restoration. And he took extremely precise photographs so that he could go back and review measurements later. His conclusion is that everything is part of what makes a Strad a Strad, but that most of the influences are relatively minor. He includes the varnish in that list. (The varnish theory dates from the early 80's, at least.) What captured his interest were the asymmetries, particularly those that remained consistent over multiple instruments. His contention is that those asymmetries are fundamentally important--and he concludes that most modern instruments are too perfect. For example, the F holes in the body of Strad violins do not line up, and the thickness of the belly isn't as symmetrical as one would assume. Most assume this is the product of hand work, and it may be, but it may also be important to smoothing out the resonances in the instrument by lowering their Q.
He came back from Italy with a whole spruce tree of the correct species that he felled himself, taking advantage of his fluent Italian to make a deal with the landowner. He thinks that's a lifetime supply. Stradivarius made 14 variations on the violin in his career; my friend's goal, stated three decades ago (and I've lost touch since then, so I don't know where he stands on it now) was to make the 15th.
Rick "and then there's the bow" Denney