Sure, but in the US, many many many more people have a state-issued ID than a federal one (a passport).
If a company needs to implement age verification, they're not going to limit their market to the set of US citizens with passports if the federal government were to offer an ID (passport) verification service. They're going to want state-run ID verification services, or, as in the case here, a private company contracted to do it for all ID types.
Then again, if the federal government (or my state government, even) offered an ID verification service directly, I would be more likely to use a product that offered it as an option, vs. one that only offered some private company's shoddy ID verification service.
But this feels vaguely analogous to the municipal broadband fights. Private ID verification companies would certainly lobby against states or the feds building their own ID verification services.