If you believe you are anonymous now, then I don't believe you have been paying attention to what the government has been able to do legally for the past 15 years.
I don't believe that this account is anonymous, but that's different than prohibiting any account from being anonymous. There are lots of relatively easy ways to be anonymous (in a city) against even state level actors (for the purposes of publishing; hiding that you exist as a person is harder). They're not free, but we're talking $50-200 in equipment, which nearly anyone could get ahold of.
I like to think I have a reasonable understanding of what the government is and isn't capable of doing, and Id point out that the last 15 years has also seen a transition from critics of surveillance speaking calmly about their concerns to filing lawsuits and hardening infrastructure against the government. The government hasn't been alone in ratcheting up their efforts, and it is indeed deeply disturbing that it seems we're on track for a showdown. Lots of people would be hurt if it came to Civil War 2: Cyberwar Boogaloo, yet how can we call ourselves Americans or patriots if we just throw away the core principles of the nation?
Other people have laid down their lives to defend that freedom, and it is our obligation now to defend it with the same passion.
Primarily, many rights are relaxed at the border (like search and seizure in Carol v United States) because the sovereign's interests and duties must be balanced with constitutional protections. If this case ever makes it to the Supreme Court i wouldn't be surprised if they rule that the government can require you to disclose all of your social media accounts if you're a non-citizen and any accounts where you do not have a reasonable expectation of anonymity if you are a citizen (I.e., they'd get your Facebook account and any account where you posted identifying details like a personal or work email but not your 4chan account).
Also, given that much of the revolutionary war propaganda and the federalist/anti-federalist papers were published under pseudonyms, Id argue anonymized political speech has been part of the American tradition since before there was a US government.
I agree, we're already not anonymous, hence your proposal is a waste of time and money.