We have had the need to prove age for hundreds of years. To buy alcohol. To drive a car. To vote. We depend on government-issued documents to do this. Not sure why anyone would really expect this to change just because it's online now.
Very obviously because privacy advocates are concerned by the effects of mass deanonymization. I find it doubtful that you don't grasp that.
Older systems were imperfect and were understood to be. I've meet veterans who joined the Navy at 14 or 16. I've met many College students who can pass as old enough to buy alcohol, especially with a fake id. Dead people are sometimes registered to vote. We know this and have systems to try to catch these exceptions.
But cellphone access is different; it's assumed to be perfect, but it's increasingly being moderated by machine learning heuristics that serve as judge, jury, and executioner, severing your services if a couple of your actions trigger a fuzzy approximation to some of the training data.
AI moderation helps suppress spammers, but it's also punishing false positives, and there is just no recourse. Any ID system that piggybacks on "Apple | Google" is effectively shunning some non trivial portion of society. Governments of the people need to provision their own tech systems that are accessible to all citizens, even those who have run afoul of an AI moderation system.
Hundreds? 200 years ago most people did not even have birth certificates. I can think of multiple famous examples of people who lived in Europe 500 to 800 years ago where we don't know their real age. In existing countries with poor state capacity, a lot of people don't have legitimate birth certificates and there is some evidence that they make up their age to some degree. For example on surveys in such countries there are too many people reporting round number ages. My experience in such countries is that you can find very young looking males riding motorcycles late at night around the city and anybody can buy alcohol. That's how it was in the United States "hundreds" of years ago. Please read a book.
Maybe hundred of years, singular. And reading/watching stuff in our own homes has never required any proof of age.
Proving your age is a relatively new phenomenon. My grandmother, born in Chicago in the 1920s didn't even know her exact age. That is not at all uncommon for her generation.