Segwit is required to fixing the quadratic hashing problem
Red herring. There is no quadratic hashing problem. There is a quadratic hashing aspect, this is true. However, as it stands today (i.e., with no changes to the protocol), mining incentives are such as to render it a non-problem.
Miners will either abandon calculating hashes of such blocks, or they will be bankrupted by other miners who do.
The issue solves itself. Today. No change needed.