Rare definitely doesn't have to mean valuable. I constantly look for musical instruments. There are tons of 'rare' instruments out there that don't necessarily command a premium. Some are rare simply because there didn't need to be many of them or some quality of them limited their production. The Gibson Style O guitar is an example of an instrument that while gorgeous and a fairly innovative piece, they don't command a premium simply because they don't produce a widely liked sound. Harp Guitars..... there just weren't many people playing harp guitars. They're rare and can command a premium among harp guitar players, but by comparison to similar standard guitars of the same era.... not even close.

rare doesn't mean desirable, but desirability can make something rare.