> The safe-harbor part isn't bad. What's bad is that people can file an obviously bogus DMCA takedown request with zero repercussions.
The takedown process is part of, and only relevant to, the safe-harbor provision.
> Companies that host content do basically nothing to actually verify that the takedown request is even from a real person (nevermind the original copyright holder).
Because not complying with a correct-in-form takedown puts them outside of the dafe harbor. The uploader can, of course, challenge the false takedown (and the host can decide they don't care about safe harbor, but they won't in practice, nor will they normally care as much about safe harbor against claims by the uploader, so counternotice compliance may be less enthusiastic than takedown compliance.)
> A better system would be one that allows the uploader to take the takedown issuer to court
You can do this. A false takedown is false, damaging statement of fact and actionable as such, it may also be actionable as tortious interference, and a number of other things.