A move has me thinking of a CD changer....?

Bits are bits. Whether played back from an optical disk (CD) or a hard drive/SSD it's still the same data! Digital is NOT like analog where every copy results in degradation! Those who claim to hear an "improvement" with changing data storage are plainly experiencing confirmation bias.

Get a 300 disc Sony changer. If you want FM quality, even a cheap CD player will get you there (actually even cheap players can sound good). Of course keep a high end single disc player for critical listening. 

I think it would be helpful to know a bit more about what you are looking for, such as: how much have you budgeted for the changer?, how many CDs would you like it to hold?, are you willing to buy something used?, what do you currently use to play CDs and are you hoping for something that is better than this or are you willing to sacrifice sound quality for the convenience of the changer?  I believe that the largest changer, a Sony,  holds something like 400 CDs, but, I don't know when that machine was last made.  

I am very much a CD person, but, I've ripped them all to a server (still keep the CDs).  I don't know how large is your collection; mine is about 5,000 CDs.  From a practical perspective, it is not easy browsing my collection, finding what I want to play, or returning CDs to their proper location in my collection so having everything organized on an iPad, with multiple ways to search for music, ability to make play lists, etc. has become more than a convenience, it is pretty much a necessity.  Particularly with Jazz, it helps that one can search the artist and find CDs where the artist is not the headliner under which I would have filed the CD physically.

Is there a reason why a changer is more desirable than a server?

For me all CD changers I've had were notoriously unreliable, but never had a Sony. I'm in the belief that streaming or putting them on a dedicated server would be the better option.