So, it wouldn't surprise me, if the current administration would at least attempt such ideas.
More importantly, it's purely a private business asking for your ID in this case, and only as an age check. In the vast majority of cases they don't record or really care about anything except your date of birth. No bar I've ever been to kept any kind of record that would have enabled them to tell the government that I had visited the establishment.
Either way, I routinely get comments about where I live, how my hair looks now, my birthday (coincides with a major date in the US). It’s very low level invasion of privacy, but most of the time I don’t want to small talk at the grocery store, I want to finish what I need to and go. N=1 and all that, but I get the point. At least no one under 21 ever drinks here.
Not that the UK and USA don't have some problems in that area