I'm less concerned about the theoretical limitations of types that you seem to be talking about and more interested in looking at concrete real-world applications where you think you need dynamic types and seeing exactly what we can do to address them with a type system. I know there exist things that are difficult or maybe impossible to define types for (the Y combinator for instance, or possibly this assoc-in). My argument is that you don't need this power. I don't care whether difficult to type things exist, I care about whether real-world problems require them. I have yet to encounter one that I felt requires the same amount of dynamic typing power that you seem to be arguing for.
See this thread for some concrete examples:
https://www.reddit.com/r/haskell/comments/792nl4/clojure_vs_...