Commerical PICO-8 games are a minority but they exist. PICO-8 can export a standalone Windows, Linux or Mac executable, or a web page. The license explicitly grants the right for authors to sell exported games.
Mastodon uses an HTML microformat called h-feed for federation of user feeds. h-feed is based on hAtom, which is a microformat encoding of the Atom feed format. So your idea isn't all that far off from how the most popular federated social network system is designed (though there's more to it).
> I could imagine an extension that's modal and allows its own plugins to be written in JS and then loaded. This doesn't seem at all to be a fundamental limitation, just "Vimium et al aren't designed this way."
Currently yes. When Chrome eventually mandates Manifest V3 extensions, they will no longer be able to run code not contained in the signed extension package.
https://openmw.org/2019/time-to-make-stuff-official/