If having code work almost everywhere is important for a project, that project will be using vanilla ES3-5 JavaScript for the next 10+ years. Maybe not the latest startups but all sorts of enterprisey ancient stuff that needs to run needs some path forward. If typescript can provide that it will become the lowest common denominator at any company that ships both new and legacy codebases.
Typescript to JS transpilation is extremely similar to the strategy that produced C++ from C. We know it will work, and it's been done before to great success. C++ isn't perfect but I think everyone agrees it's definitely a lot nicer to work with than C, and that's exactly how I describe Typescript as well