Mozilla is the company we trust when it comes to online privacy, security, and the Open Web. Having a web service like Mastodon Social under the Mozilla umbrella will guarantee more freedom of expression on the Open Web.
I personally believe that it should be part of Mozilla's mission to support and protect Federated Open Source Services, that are not controlled by a corporation.
In fact, Mozilla already supports one of those federated services.
My idea is to create a web portal called Social.Mozilla.org where users could sign in with their Mozilla Account and enjoy a Twitter-like social experience powered by Mastodon's code.
The source-code of Mastodon is accessible on Github, and there are plenty of guides about how to install it and maintain it.