Unless something has changed a lot, C++ templates at least only used to be Turing complete if you assume you're allowed unlimited recursive template applications, and compilers were free to restrict that (and did). Has that changed?

In theory I agree with you that this is horribly ugly - I very much prefer simple grammars (the irony being my favourite language to use is Ruby, which has an atrocious grammar). In practice these parses are rarely that hard to resolve.