Humanity developing a quantum computer strong enough to break ECDSA seems far more likely than someone finding an effective alternative to Shor's algorithm for classical computing tho.
It is exactly the opposite. Quantum computers are likely never going to do any useful cryptography related stuff. And Shor's algorithm is yet to be implemented, it exists just on paper, and very small and truncated versions happened. With current hardware, to even have a theoretical chance at ECDLP, one needs more than 28*10
15 qubits - this is 28 Peta qubits. Even with ideal, zero noise QC, one needs 126*10
9 Toffoli gates.
And something more about the all-hyped Shor's algorithm:
We consider Shor's quantum factoring algorithm in the setting of noisy quantum gates. Under a generic model of random noise for (controlled) rotation gates, we prove that the algorithm does not factor integers of the form pq when the noise exceeds a vanishingly small level in terms of n - the number of bits of the integer to be factored, where p and q are from a well-defined set of primes of positive density. We further prove that with probability 1−o(1) over random prime pairs (p,q), Shor's factoring algorithm does not factor numbers of the form pq, with the same level of random noise present.
Well, looks like even quantum error correction wouldn't help with ECDLP. All quantum hope is gone.