Mumble is great, but there are some things that people have come to expect from group chat services that it is not designed to do. For example, running in a web browser, persistent message history, and multi-device access to a single account. Adding such things would be no small amount of work, which is probably the main rason it hasn't been done. (And, of course, the changes required would make the result incompatible with Mumble.)
Considering what exists today, I think Matrix has the best chance at becoming a Discord alternative. It already has a lot of the needed features, The new voice/video system (now in beta) looks very promising. And, of course, it also supports self-hosting and end-to-end encryption, both of which Discord lacks.