1) Yeah that works great until someone uploads content about children being sexually abused and you can't take it down because taking it down is a non-neutral action (censorship).
2) Same, but non-consensual pornography of someone's ex.
3) Same, but advocating a clear and immediate desire to commit violence.
4) Same, but "fighting words" (a well known exemption when said to someone's face to free speech protections).
5) Same, but obscenity.
There are some very, very massive flaws of that nature with your position and I'd continue but I think you are getting the idea. Such things don't only impact the speaker and therefore create a situation where the provider should (in theory) censor them.
Similarly, such things have been ruled to be outside of the bounds of "free speech" in the US by the judicial system.