I'm not too familiar with cryptocurrency or generally blockchain implementations, so I wonder: shouldn't it be normal that at least the reference clients of any such protocol should be proven correct, and follow a rigorous scheme accepting contributions?

I mean, all the mathematical rigor and proofs of the underlying theory and protocols are basically useless if the rigor isn't carried over to at least the reference implementations. (If people choose to use alternative, non-proven clients, fine, that's their own decision and risk.)