When I was in (secondary) school in the UK, we could get served beer in the pub at lunchtime while wearing school uniform! Doesn't get much easier than that!
I'm much older but I think 16 is old enough for a beer. I didn't when I were that age but I don't begrudge them their beer.
And it's not like the law will stop it from happening anyway.
I have seen this with several European friends who relocated to the US and found their relationship with alcohol turning dark.
My personal theory is that life in the states may be on average more stressful than in Europe, perhaps due to lack of healthcare, at-will employment, etc., and this life pressure causes people here to be more at risk of self-medication problem drinking.
Most other developed countries get by just fine with a much more relaxed attitude. Demanding identification and legal documentation for every little thing is excessive and imposes a compliance burden on everyone. It's fair in the sense of being non-discriminatory, but unfair in the sense that it creates a massive aggregate burden, reduces privacy, and institutes authoritarian presumptions.
If the person manning the self-checkout operations thinks you look awfully young to be buying alcohol then they can always demand to see your ID.
Simple.
Far more harmful is self-checkout without a discount for free labor or treating your customers like criminals when they leave the store with their own property.
You seem to have missed the part where I do not want to ask permission of the government for every little thing. I'm well into middle age and do not appreciate having to seek governmental approval for what I consume. I am fine with some products like alcohol being subjected to taxes to balance out negative externalities. I am not fine with the idea of showing my papers on demand.
Using your UK credit card? If so, that's an age check in itself.