Making proof assistants more user-friendly is definitely a worthy goal to pursue!
Something you don't say in your video is who you consider to be your users. You mention both proofs in mathematics and formal verification of software. These are fundamentally the same problem, but the users interested in these two domains have quite different prior experience, so maybe being friendly to one doesn't imply being friendly to the other. Another consideration I see rarely made in this space is that readers of proofs are also a kind of users, even if they never touch the proof assistant themselves.