A lot of people have talked about the possibility of forking Mastodon to get the many improvements their communities need. Making such an effort successful is another discussion entirely.
I don’t really see the point in forking a project like Mastodon unless you are already deeply involved with its development. It doesn’t do enough that you couldn’t rewrite it better (as in in a way you understand better and with lessons from the original taken into account) in the time it would take you to fully understand all the details of the existing code base.
It actually does have that nowadays, it’s just that the feature requires Elasticsearch to work, which is one extra piece of infra for admins to worry about.
It is about as common as using a database server for content though to use something like ES, Solr or similar software for search.