Quantum vs ZKP? I don't think you understand what ZKPs are.
ZKPs excel at proving statements without revealing data. It helps in enhancing privacy, scalability, and functionality on Bitcoin like PoR(proof of reserve) for exchange audits
You summarized problem with OP's comparison nicely, although AFAIK usually it won't help scalability since cryptography for ZKP have bigger size than non-ZKP ones.
Actually, how critical is this quantum threat?
Nobody knows for sure when will quantum computer is mature enough to pose realistic threats to cryptography used by Bitcoin.
Could ZKP be its successor?
No, what needed is quantum resistant cryptography. While you can find cryptography that have both quantum resistant and being ZKP, it's unlikely to be chosen to replace ECDSA/secp256k1.