It "just" makes Twitter readable to the Internet at large.
"At large" is a strong term given the average person (even the average Twitter reader) doesn't know what it is ;)
I think you misunderstood. Twitter is almost unusable without an account, and the website is very slow. Nitter makes it usable for the majority of us with no twitter accounts, and/or relatively slow devices.
Also, you can host your own private nitter instance and follow accounts using rss.