Yeah, the US will never adopt a law like that. Anonymity is extremely protected by the Supreme Court, because the founders wrote and distributed pamphlets anonymously in support of the Revolution.
And yet the US has all kinds of surveillance apparatus to de-anonymize internet users...
Even if you take the parallel construction angle, no politician except maybe a dinosaur that is super-secure in their position (on the federal level that would be people like Pelosi, Fienstien, etc.) is going to tolerate that because if the other side can prove you knew then you're not going to have a job after the next election.
Obviously we need to remain vigilant but there are existing feedback mechanisms that generally prevent wide spread abuse.
Politically, I don't know how it's possible to look at the current climate and think it will work against mass surveillance. Politicians will just shy away from directly confronting the issue. Whenever any spotlight gets close, the agencies will continue categorize it as national security / tough on crime / etc. The best political ally is seemingly the judiciary, and that itself will only slow things down.
This is codifying forced attribution for everyone into law.
The US philosophy is to do passive surveillance and assemble the pieces after the fact, rather than mandating ahead of time requirements. Which means that US-based services will continue to be unhindered by such requirements, appearing "anonymous" to the rest of the world.
As more people globally are turned off by ID requirements, if they're able to flee to US services, then they're actually walking into a more sophisticated passive surveillance flytrap. USG will have ever more surveillance over other countries, without even having to clandestinely place taps.
Close allies will be given access through FVEY and the like, making that relationship even more lopsided. But allies' domestic law enforcement won't be, so they'll still be clamoring for more simplistic mandates requiring ID, further driving the process.
To clarify, anonymous speech is protected by the First Amendment.
With certain limitations. If someone anonymously offers drugs on the 'dark web', that is not protected, of course.
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