Can we actually prevent children under 16 from buying beer?

If they are persistent enough, no. But then everyone knows it's not going to stop every child in every situation. It sets a president for what society thinks is a sensible limit though, and society raises children not just individual families or parents.

Do we want kids becoming alcoholics? Do we want them turning up drunk to school and disrupting classes? Do we want to give parents trying to do the right thing some backup? So they know that when their kid is alone they can expect that other adults set a similar example.

Sure, you can't stop a kid determined to consume alcohol. But I think the societal norm is an overall good thing.

The same should be applied to the online space, kids spend more and more time there. Porn, social media, gambling etc. should be just a much of a concern as alcohol.

Is there actually a difference between transactions between humans in meatspace (getting a government ID, then using it at a store) and age estimation algorithms?