I believe that the "one account = one real person" policy actually makes things worse.
Regardless of what Zuckerberg claims to believe, in real life I have multiple "profiles". For example, I don't debate Java programming with my family members, I don't debate politics or religion (or generally any opinions, because no one knows what will become a hot political topic tomorrow) with my colleagues, etc.
Similarly, I have different rules for reading stuff. I hate memes, but if my cousins post some, I am not going to block them like I would most other people; I will just sigh and scroll down. More importantly, I do not want to read stuff from all my social circles at the same times; sometimes I am in a mood for family stuff, sometimes programming, sometimes other things.
Even better would be to have advanced tools (but with simple user interface) to specify what I want to read; e.g. "what my cousin wrote, but not what someone else wrote and my cousin shared"; to filter posts containing certain words, etc.
Merely removing anonymity will simply divide users into two groups: those who care about not getting fired tomorrow so they only post completely unobjectionable politically correct vanilla stuff, or those who are not very smart or young and inexperienced or too rich to care about what other people think, so they post anything that comes to their minds.