Are you suggesting fixing malleability by storing transactions as they are now and omitting signatures from the txid calculation? In effect, a hard fork.
Yes. That fix should be done by a hard fork: because the code will be much cleaner, and because hard forks are safer than soft forks. (More precisely: ensuring that old versions are inoperable after 3-4 releases is safer than deploying changes to the protcol without alerting users, and letting them discover later that they must upgrade to understand why their transactions are not confirming anymore.)