People do this with musical instruments too. I argue (after the first year of a new instrument, where it settles etc) it has more to do with learning how to draw the best sound out of an instrument, and less about the instrument improving.
And the bridge might settle a little and the pegs need to settle in, etc. Any instrument that can be affected by humidity and temperature can be affected by time at humidity and temperature. I'm pretty sure there's not a lot of point in "burning in" a brass instrument but I've been wrong before.
Some brass instruments are valued because of better quality metals (more pure alloys - a bit of any oxymoron i know -, different valve systems, etc), but woodwinds almost exclusively devalue because they fall apart (wood vs. hot, sticky, bacteria infested air), and brass instruments tend to devalue on the whole as well. The good news for them is that new wind instruments are considerably less expensive than new string instruments. A custom made, top-of-the-line Trombone will cost you less than 10 grand unless you're REALLY trying to burn your money. Oboes and Bassoons are more expensive, but also tend to have more resale value as second-hand for students. to compare oranges to oranges, a new, top of the line Bass could cost you over 40k, or more. And basses are considerably cheaper than their smaller cousins. String instruments change a lot in the first 2 years. I can only really speak for basses, but having owned two new instruments, the Low end in particular takes time to develop. Slowly you start to notice the D string sounding great, then the A string. Eventually you start to get some real subterranian shit going on, and the viola section can feel you in their chairs. My current bass just hit it's first birthday a few days ago, and it's low 5th string is still working on being "played in". I've heard, for string instruments, that the process has to do with "disorganizing the longitudinal wood fibers", but fuck, idunno. Bass sounds good, I play it, i get better at playing the bass, one day I don't suck (hopefully).
yaaaay lack of resale value. at least I have the consolation that if I fail as a musician and a person I can sell my bass and get a year's worth of living out of it. Either that or I can burn it to keep myself warm.
I remember taking music in school. I came to realize that each instrument had its own unique voice. The slightest damage, say a tiny dent, will change that voice. I think you are right about the "burn-in" idea for instruments being not for the instrument but for the player. Burn-in is starting to become an over used term. Like "love/hate."
Some people think burn in of headphones is exactly same thing - it's your ears (or rather brain) getting used to the audio profile of the headphones and not the headphones sound quality improving over time.