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What are Unix man-pages but comments about the APIs they describe? Are you saying you would prefer to replace them with the TypeScript type-language?
As I see it TypeScript is a a solution to the problem of how to describe a function, what it does, what it expects from its arguments and what it returns. That information can often be clearly and simply expressed with a comment, rather than with a complicated type-declaration. And type-language only describes the syntactic behavior of a module, not its semantics.
When type-declarations become more complicated than the code they are describing I think we're at a point of diminishing returns.
The other purpose of type-declarations is to catch errors. But if a declaration is very complicated how can we be sure there's no errors in it?