As described in phabricator, the front end is far from what users expect from a modern player. This needs to be addressed, but if this is done within TimedMediaHandler or within a new extension is strictly a technical decision. The important thing is for resources to be allocated, as video becomes more and more important, even for Wikipedia.
One point I would like to raise is the ability to upload non-free formats. While there have been a community consultation and the proposal was rejected, the software should have the ability to allow such formats, should the community reconsider.