(author of the blog post here)
"just compile when you know the types" is not a good strategy for Python.
My EuroPython talk "Myths and fairy tales about Python performance" explains many reasons why Python is VERY hard to optimize:
https://lwn.net/Articles/1031707/One big advantage of tracing JITs is that they are generally easier to write an to maintain.
For the specific case of PyPy, it's actually a "meta tracing JIT": you trace the interpreter, not the underlying program, which TL;DR means that you can write the interpreter (which is "easy") and you get a JIT compiler for free.
The basic assumption of a tracing JIT is that you have one or more "hot loops" in which you have one (or few) fast paths which are taken most of the time.
If the assumption holds, tracing has big advantages because you eliminate most of dynamism and you automatically inline across multiple layer of function calls, which in turns make it possible to eliminate allocation of most temporary objects.
The problem is that the assumption not always holds, and that's where you start to get problems.
But methods JITs are not THE solution either. Meta has a whole team developing Cinder, which is a method JIT for Python, but they had to introduce what they call "static python", which is an opt-in sets of constraints to remove some Python dynamism to make the JIT job easier.
Finally, as soon as you call any C extension, any JIT is out of luck and must deoptimize to present a "state of the world" which is compatible with that the C extension finds.