I know of a few folks in the IndieWeb and WordPress communities like Ryan Barrett (with FedBridgy) and Mathias Pfefferle (with OStatus plugin) who are actively working on helping bridge the technology between websites and the Fediverse so that one could use their WordPress install as a stand-alone “instance” of Mastodon.
It already seems somewhat obvious that moving from Twitter to Mastodon is bringing along some of the problems and issues that Twitter users are facing, so being able to use your current WordPress (or other) website to interact with other instances, sounds like a very solid idea. In practice, it’s the way I’ve been using my website with Twitter 1 2 (as well as Google+, Instagram, Facebook and other social silos) for some time, so I can certainly indicate it’s been a better experience for me. Naturally, both of their efforts fall underneath the broader umbrella of the web standards solutions generally pushed by the IndieWeb community, so I’m also already using my WordPress-based site to communicate back and forth in a social media-like way with others on the web already using Webmention, Micropub, WebSub, and (soon) Microsub.
These federation efforts have got a way to go to offer a clean user experience without a tremendous amount of set up, but for those technically inclined, they are efforts certainly worth looking at so one needn’t manage multiple sites/social media and they can still own all the data for themselves.