From what I've heard about things like eIDAS there is considerable technical competence behind the specifications for these laws, I would expect there to be mechanisms for cryptographically secure offline validation.
I don't think it will fulfill that purpose in practice. The name plus date of birth is a very good tracking identifier and people will be still giving DOB to these companies.
Basically, with the right cryptography, my app can prove my license is valid without revealing any PII. Or in the case of eIDAS, binary questions like "is rekoil 18 years or older?".