Viscoelastic polymers are poison for stringed instruments, because they have very high damping coefficients. They turn the precious vibrational energy from the strings into useless heat. Only cheap mass-produced instruments are finished in polyurethane; quality instruments of traditional wood construction use a shellac-based finish (sometimes nitrocellulose lacquer on guitars), which have lower damping and can be applied more thinly in practice. In the context of high-quality instruments, the difference is not subtle.
Wood instruments need a finish to protect them against moisture, but that isn't an issue for CFRP. Any finish - especially the kind of thick finish you need to get a high gloss over woven reinforcement - makes the instrument worse for no benefit other than cosmetics. If you would choose a shiny instrument over one that sounds better, you're buying a showpiece rather than a serious musical instrument.
Epoxy is a necessary evil in CFRP, but we want the absolute highest possible fiber volume ratio. Unidirectional or spread-tow reinforcement will always allow for a higher fiber ratio than woven material.