1. Use WebTorrent[1] as the tile provider (would probably need a canonical WebTorrent server so that all tiles would always have at least one seeder).
2. A Progressive Web Map (teehee) so that users can store tiles offline and use the mapping service while offline. Obviously not a new concept but AFAIK there isn't a map provider that does it in the browser.
3. Client-side routing/navigation. This could start as a simple Dijkstra in JavaScript (like is demonstrated in [2]), but maybe could be made more powerful and capable soon with WebAssembly.
Is anybody working on these sorts of things? Is anybody interested in them? I've heard of peermaps[3] but it hasn't been updated in over 6 months. I'd be interested in contributing or teaming up with others on these sorts of things.