The government already knows all of our sensitive information, so we are not giving them any information they do not already know. The government is normally legally prohibited from age discrimination, at least in regards to citizens, and has a legal duty to protect our personal information. And if you can prove that the government discriminated against you because of your age, or if the government leaked your sensitive information, you have legal recourse.
Everyday acquaintances and peer colleagues, however, have no restrictions against age discrimination or any legal duty to protect your personal information. You also have no obligation to show your ID to these people. You can safeguard your ID and only show it to people who need to see it, which generally just include the government, financial institutions, healthcare providers, the HR department of your employer (which, unlike peer colleagues, is subject to the legal duty not to discriminate based on age and to safeguard everyone's private data), educational institutions.
So I don't see how getting ID is relevant to the fact that date of birth is sensitive information that you should not need to reveal to acquaintances.