Hmmm, I have a picture of a can of worms around here somewhere...
You'll find some people who swear up and down that all solid instruments get better with time, others that it's completely mythical. Myself, I think it falls somewhere in between. I know for a fact that it sometimes happens, because I had a cedar-topped dreadnaught guitar that just opened up amazingly in the first few weeks. It was such a transition that it almost seemed like it sounded better every time I played it for the first few weeks. On the other hand, both of the Taylor guitars I've owned have changed little if at all while I owned them, and I've had the current one and played it pretty regularly since 2002.
There's also a lot of disagreement and not much proof on the cause for why some instruments, at least, "open up" as they are played. Some think it's changes in the wood itself, others think it has more to do with construction and bracing and the fact that instruments with solid tops are far more likely to be premium instruments to begin with.
My personal opinion is that some instruments "open up" and others don't. It's quite likely, maybe almost certain, that some instruments actually get worse with age and use. I think some of the idea that "solid instruments get better with age and use" is simply the fact that the majority of the sample of older instruments that we have are around because they had a good "voice" to begin with. Instruments that sucked or got worse with age tended to wind up in basements and attics and the local city dump.
BTW, in the example I cited above, the guitar that "opened up" so amazingly in the first few weeks or months was a fairly inexpensive guitar that started with a voice that was decent, but not stunning, to begin with, while both of the Taylors had amazingly good tone from the beginning.
John