That isn't a problem unless you're discussing something where anonymity is key - or it wouldn't be if the internet didn't make anonymity the rule by default. Anonymity is really great for private citizens, but people trying to spread information need to be held to a higher standard since their words shouldn't be preemptively censored but must be held to account after the fact.
Oh also, taking away anonymity is quite dangerous as well - there isn't an easy answer here.
I'm not sure I'm convinced that taking away anonymity fixes the problem. We have very prominent politicians who are driving entire political campaigns around this strategy of ignoring all fact.
I honestly think that prominent politicians wouldn't have any willingness to adopt this insane level of misinformation if there wasn't such a general societal acceptance of it.
The people in congress that believe in jewish space lasers didn't get elected because everyone around them thought they were crazy conspiracy theorists.