Anonymous accounts should not be disallowed entirely, but they should be observed more actively for misbehaviour, including things such as spreading of miss- and disinformation and manipulative content. Sometimes individual posts does not really spread misinformation, but when you look at the bulk of the content it becomes clear that they are actually engaging in the active spreading of disinformation. This brings me to a very important point: anonymous accounts should be clearly marked as being anonymous. They should therefore not allow a profile picture.
Disinformation can also be in the form of suggestive or questioning material. E.g. Sharing a piece of misinformation and writing "interesting?" or "I really hope this is not real?". If such behaviour is consistent, then it is usually because that account is used to re-share disinformation, and if the account has nothing else of relevance. E.g. Does not have any authentic connections outside of this "conspiracy" network, then obviously it has no authentic purpose on social media.
So while anonymity is important to defend, we also need to identify the bad actors that abuse it. For this there are some behavioral patterns that are easy to identify, and this could, to some extent probably be automated already now.