What's the point? Anybody running a faster system can just slow it down to pretend to be the old, slower one.

Quantum computers don't actually help you find SHA256 collisions. Even if they did, you could just go up to SHA3 with 512-bit output or something.

ECDSA was probably chosen over RSA because ECDSA keys and signatures are much smaller than RSA keys and signatures, at the cost of being somewhat more computationally expensive to verify.

Your statement about "phi's relationship to scalar and vector fields" reads like nonsense to me.

I don't understand. SHA-256 has nothing to do with computing Euler's totient function, and neither does computing the GCD (well, you can use it to compute the totient function, but it's not the most efficient way). And I'm not sure how you'd use the totient function as a proof-of-work.