I mean the elder wand is so old it has a mythology. I think they are effectively "immortal" and never wear out unless they get damaged somehow.

Afaik, there's no in universe, canon answer.

But you'd be amazed how long well made wood items can last, and most wands in HP were mainly wood.

There's examples of things made of wood lasting thousands of years. With proper care, and you'd think wizards would put that effort in to something so important, there's no reason given in the books or movies a wand couldn't last indefinitely unless damaged by abnormal circumstances.

Just as an example, my mom has a kitchen knife that was made in the 1700s. It isn't used any more, but the handle of it is in great shape. No cracking, no splitting, and only minor wear. My house has wood floors that are creeping on 200 years old, and they've been used, in the section of the house where they are.

Wands don't get the same kind of wear and tear at all.

From the way the movies and books make it seem, wands being passed down is likely common, but not necessarily in every family are there enough to go around, so you get wands being reused like the Weasleys did. One kid graduates, the next kid gets the wand, and the now adult wizard gets their own, or that's the way it seems to work.

We know that wands choose their owner, and can change allegiance.
Perhaps if a wand rejects (or is won from) it's owner, it can become a hand-me-down.
Also, witches/wizards die. At which point the wand can be a hand-me-down.
It might also be that the perfect wand is too expensive, so the witch/wizard buys a cheaper "good enough" wand to get through school, then decides to treat themselves later when they have more money.
Perhaps a family has a cheap wand for their kids first year(s) at school incase they break the wand. When they get older, they get a "proper" wand and the cheap wand can go to the next kid.
I'd imagine that families would share these hand-me-down wands with other new families, similar to cots/prams/clothes etc.