I think "unknown type at compile time" and "JIT-able constructs" are opposites. You'd end up with a tracing JIT that compiles the same set of code in different, specialized ways based on runtime determination of the the input types as though the lang was static. Which is basically what we have today. You can have optionally typed languages, but you still have to write your runtime and compiler to the lowest common denominator, so you probably want to go more strict if you care about your (runtime or compile-time) compiler and runtime performance (as the Dart devs learned IIRC).

I would assume "JIT-ability" is proportional to the immutable input and output knowledge of the code to be compiled.