It comes back to reputation. In the real world, we build up a reputation and people can choose to trust us based on it. That also means that they get to know us. I personally like being able to interact with people that I've built up a positive relationship with. Why doesn't that carry over to the virtual world though?
I think everyone's view is tinted by the over-collection of data that some companies are doing. A real-life analogy would be having someone record everything that you do. We've come to accept that to an extent when going into stores, but probably wouldn't hang out with a friend that did that. I don't think the best solution to that is to put a bag over yourself and change your voice so that you're anonymous but still hang out with that friend -- I think it's to tell your friend that you don't want to be recorded. If some service is recording you too invasively, don't do business with them. If you don't know who is recording you, get your government to pass a law like GDPR.
If you want to live in a world without reputation, there will be drawbacks. Attackers will be indistinguishable from regular users, so you have to treat regular users as if they could be attackers; you can't have a tiered approach. The person banned for posting threats (or worse) or otherwise misbehaving on a message platform will be indistinguishable from a new account. The brute force attack will be indistinguishable from the legitimate user. Etc.
To throw out the whole concept of reputation so that you can be perfectly anonymous seems like the wrong solution to the problem.