This ...
might be possible, but the performance would indeed suck; you’d need to essentially ship half a compiler toolchain in your polyfill, and ensure that it gets run separately, non-async, so that the browser finishes installing it before attempting to interpret any more tags. (And, presumably, all of your app’s source would be in the next script tag, so that your app can take advantage of native bigints; so your app wouldn’t load at all until the toolchain had finished bootstrapping.)
I’m guessing this has been done, to let the browser run—without backend compilation— where foo is CoffeeScript or TypeScript or ClojureScript or what-have-you; but this one would be especially bad, because the thing it’d be targeting would still be Javascript, and so you’d have to rewrite all Javascript sources you encounter, with most of them likely never using native bigints but suffering the double-parsing overhead anyway.
Oh, and you’d have to override the ES6 module loader with one that also rewrites what it loads. Ugly.