What do you view as alternatives? It seems to me like this is a huge improvement on unlimited vacation, so you should add suggestions for improvement rather than knocking it down.
* Vacation time use stats can be shared internally if your culture demands it, but should never be shared externally except in aggregate (violates the privacy of your employees)
* Don’t advertise unlimited vacation, because it’s not truly unlimited
* Properly account for staff being out in your capacity planning. If someone isn’t able to take their vacation time because there isn’t sufficient slack in the workload, you have failed and have essentially taken their compensation from them
Bonus points: Parental leave (offer what you can afford if you feel you need to compete on that benefit)
Some sort of vacation budget system, where you can take a certain amount each time period.
(Perhaps a certain amount could roll over from time period to time period.)
That manages expectations, and assuages anxieties about taking vacation. No need to constantly question "Has Mary/Dave/I earned this?" Big culture win.
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Apologies for the snarkiness, but this ultimately seems like a self-imposed problem.