I disagree with the OP comment that this practice is a thinly veiled attempt to rationalize buying expensive bottles - the rationalization is not veiled at all.
I agree with David L about including riesling - it will age, and the kids will like it before they’ll like the other stuff.
Despite my first comment, I also agree with Fu that it’s a hopeful gesture re their future love of the stuff.
We have a '93, a '95, a '98, and an '00. I made a point to buy a handful (6 bottles per kid, some large format) of wines outside our normal price range to open at 21, 25, 30, 40, etc.
I also made a point of opening a birth-year bottle from our regular stash every year on their birthdays up to 20.
As for the kids’ reactions - I would say that when they were younger, one (who to this day doesn’t like even to sip any alcoholic beverage) really got a kick out of “her” birthday wine being from her birth year, even though she didn’t drink it. The others kind of nodded to Dad’s weird habits and eye-rolled and tasted sips and generally hated them (all dry reds).
Things eventually changed. The '93 really liked the Giacosa Barbaresco on her 21st and the Haut Brion on her 25th, and has saved both bottles as souvenirs. She’s unlikely ever to be a wine geek, but now drinks the bottles I open with pleasure. The '95 was lukewarm on the Angelus we opened for her 21st, but has started enjoying reds more since then and I’m sure will enjoy her future “milestone” bottles.
Having failed to do so timely, I did pick up some '93 and '95 rieslings on backfill specials (Garagiste, etc.) and they have loved those. Good college graduation wines.
The '98 is the non-drinker, so those we’ll just enjoy in her presence, and the '00 is too early to tell but I’m hopeful.
No regrets in buying and opening any of these, and as they’ve gotten old enough to really understand the concept, I think the kids appreciate it.
I also started loading up on wedding year ('88) wines way too late to start drinking them at early anniversaries, but we had one for our half-25th, and then for every anniversary from the 13th to date. Each a different wine, all the empties decorating our dining room shelves, and enough in the cellar to take us through our 50th. Fun stuff.