They can't support C extensions, which are basically required for any real world Python.

Pyjion is a Microsoft CoreCLR JIT that can support C extensions. That's Python's next great hope for speedup via JIT.

Pyjion is C Extension based JIT for CPython. Pyjion only uses CoreCLR RyuJIT as a JIT compiler backend. It is NOT aware of .NET types at all.

Note that you can use pythonnet for interop between CPython and .NET for both embedding and extending.

Works has stalled on Pyjion and there's not a lot of contributors or money behind it at all. Don't let the hype get to you. As it was fairly obvious with Pyston, PyPy is still where it's going to be at.

DLR is just dynamic runtime for dynamic languages, including IronPython, IronRuby, PowerShell, COM interop calls. JIT is for CLR runtime to compile IL byte-code.