No. If its not good for the public, then either don't use it, or pass legislation to ban it. subsidizing a business because they can't do it is wasting tax money for a video game.
Regulating that vast swarms of businesses need to make their own age verification system seems like a waste of economic value. Especially considering how many normal tasks that near everyone does would also benefit from such a government system: Loans, Rentals, Housing, etc.
You would also only need to provide the evidence once to the governing body that gave it to you in the first place, instead of giving it to dozens of companies.
My taxes shouldn’t provide economic value to random companies who want to verify age, and creating a centralized identification system that is available to non governmental entities is ripe for abuse.