Static analysis is not just about inferring types and hot paths for optimization. For that kind of stuff, a dynamic analysis is most of the time way better (lots of JIT compilers with speculative optimizations prove this point). There is another goal where static analysis shines: verification. If I'm writing a somewhat critical application, I want to make sure that it behaves according to my intent in all cases. For example, if I'm writing an airplane sofware, I want to make sure that it will at least never invoke any undefined behavior (this is done in ASTREE project). Static analysis is a powerful tool to give such guarantees in many cases.

Some highly dynamic language features make analysis really imprecise or really hard (in terms of computation cost). There has been quite a lot of work on making static analyses that can handle such language features (for example control flow analysis helps analyzing code that uses dynamic dispatch or closures a lot but cost of the analysis is exponential in terms of the precision level most of the time). Sometimes people tackle analyzing highly dynamic languages like JavaScript but at a huge time cost in certain cases [1]. I'd prefer using a language designed with static analysis in mind if I were to prove certain properties about my code.

[1]: http://www.cs.ucsb.edu/~benh/research/papers/dewey15parallel...