[armchairhacker]

Unfortunately a big issue in TypeScript is that objects can and surprisingly often do have the completely wrong type. Some libraries even blatantly violate their TypeScript types. So any optimizations which take advantage of TypeScript types are likely to lead to very hard to debug behavior.

A better option is to make/use a language which interfaces well with JavaScript but is not JavaScript and actually checks it’s types. If the type system is actually be sound, and any code going in from JavaScript is type-checked at runtime, then compiler optimizations are reasonable.

As for your last point, I know that JIT-compilers like V8 can and do infer types at runtime (e.g. by noticing if a particular variable or function arg is always set to the same type) and will compile specialized function overloads which take advantage of the inferred type for optimizations (e.g. using fixed-width integers even though all JavaScript numbers are doubles).