Earlier quoted context omitted.
AFAIK good JITs like V8 can do runtime introspection and recompile on the fly if types change. Maybe using the type hints will be helpful but I don't think they are necessary for significant improvement.
Are there any benchmarks that give an idea of how much this might improve Python's speed?
That's for this benchmark:
https://pyperformance.readthedocs.io/
Note that this is with a relatively small investment as these things go, the GraalPython team is about ~3 people I guess, looking at the GH repo. It's an independent implementation so most of the work went into being compatible with Python including native extensions (the hard part).
But this speedup depends a lot on what you're doing. Some types of code can go much faster. Others will be slower even than CPython, for example if you want to sandbox the native code extensions.