There's not much of a point. It'd just slow movement on Typescript itself. Unless of course fast-moving, transpiled Typescript started being transpiled to browser-acceptable Typescript, i.e. transpiled back enough to where most browsers can parse it. But at that point, why not just do it the way we're currently doing it, targeting JavaScript? Also it'd just make web dev even more confusing for newcomers than it already is.
I don't really see an issue with treating JavaScript as something of an "assembly of the browser," in that anyone can make their own language and target it.