Comment by Gaelan

This is essentially doing that—it would allow browsers to parse and run TypeScript. What it isn't doing is actually having browsers do type checking, for good reason: the TypeScript type checker is a large and complex piece of software, so browsers would either have to incorporate it (and they're probably not excited to have a large chunk of JS code in the critical web-page-rendering path, nor would they be excited to have a critical chunk of the browser with a single implementation), or reimplement it themselves (which would be a huge amount of work, and make changes to the language much slower and more difficult).