Thanks for the feedback, the web UI does have a gallery link [0] with a few interactive examples [1]. I agree though, a screenshot like this would be a good addition to the homepage.
Yes, that's roughly accurate. Jan Pöschko (the creator of Mathics) went to Wolfram in 2012 and I went to Google at the end of 2016. Since then it's been largely unmaintained as I don't have the time to work on it unfortunately
The main issue was that generating the tables was extremely slow (~15mins). We solved this by packaging the tables, but when the version of ply changed a table regeneration was forced on our users.
The recursive descent parser was also simpler and significantly more performant.
The web interface does have inbuilt docs. Code introspection and tab completion are coming as part of the new interface (in progress) see https://github.com/mathics/IMathics
[0] https://pasteboard.co/IdIaJNo.png [1] https://pasteboard.co/IdIc7dc.png