Yes it's planned. Should work in theory, but no one tried before.
Maps are so often done as native apps that to my knowledge no one tried to just use the PWA capabilities to cache tiles on the Web. Of course what's hard is cache invalidation. Does the user want to update the tiles ? Never ? Daily, weekly ? Only some regions ? Or manually ?
Here's an issue about that : https://codeberg.org/cartes/web/issues/1078
It's in French, unfortunately Codeberg has no auto-translate capabilities yet.
FWIW, I have an experimental open-source implementation of offline-capable PWA protomaps. Haven't advertised it much, because I haven't sorted out performance (particularly on mobile), and it's a bit buggy still. Also, don't have cache invalidation. But it does work. Usually. xD
app: https://maps.bpev.me
source: https://tangled.org/bpev.me/maps
Based on results from indexeddb pmtiles work:
https://github.com/jtbaker/pmtiles-offline
https://github.com/protomaps/PMTiles/issues/395