What are you looking for? If you want to be anonymous, your are SOL unfortunately. If you are looking for a less crappy browsing experience than Twitter, and Nitter filled that void, you can find forks which fetch content with your Twitter account. Setting up for local self hosting doesn't take a lot of minutes.
The question is whether or not they'll continue to develop Nitter just for people who want to run it locally. Twitter's page layout & functions get updated and changed CONSTANTLY. If someone isn't updating Nitter regularly it will become depreciated very quickly.