If you only know the birth year and keyed 99 as the month for unknown, then your algorithm would determine they were of a correct age on the start of the year after that was true, which I guess would be what you want for legal compliance.

If you don't even know if the birth year is correct, then the correct process depends on policy. Maybe they choose any year, maybe they choose the oldest/youngest year they might be, maybe they just encode that as 0000/9999.

Again, if you don't know the birth year of someone, you would have no way of knowing their age. I'm not sure that means that the general policy of putting a birthday into their ID number is flawed.

Many governments re-issue national IDs to the same person with different numbers, which is far less problematic that the many governments who choose to issue the same national ID (looking at you USA with your SSN) to multiple individuals. It doesn't seem like a massive imposition on a person who was originally issued an ID based on not knowing when their birthday to be re-issued a new ID when their birthday was ascertained. Perhaps even give them a choice of keeping the old one knowing it will cause problems, or take the new one instead and having the responsibility to tell people their number had changed.

Presumably the governments that choose to embed the date into a national ID number do so because it's more useful for their purposes to do so than just assigning everyone a random number.

Or have the opportunity to scam people into thinking you’re a different person. (E.g. take a $1M loan, go bankrupt, remember your birthday, and take a loan again.)