If .gov == bad guy then you’re screwed whether or not you leave a digital trail on social media because you’re already leaving one anyway (unless you’re a marginal outlier that isn’t worth considering for this “problem”). If that’s your threat model then you’re either super-important or I worry you’ve been sold a scary story by social media algorithms.
On the other hand, the idea that this is an impossible tech problem to solve is also disingenuous. My point is that it could be solved. And quickly and easily too. If the incentive model were there. And whilst I’ve not given the solution a huge amount of thought (I’m not actually that interested in solving it) I’m certain that an authenticated assertion could be made that wasn’t directly attributable to an individual - i.e., a mechanism could be developed that would solve for both problems.
Which brings us back to the fundamental point here: the people who would need to implement the solution have no incentive model in place to motivate them to do so.