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.)
I've seen enough in this thread to convince me that that approach would make deployment a disaster for bitcoin. People would lose funds.
One example gmaxwell gives: all presigned nlocktime transactions would be broken. For users keeping these in storage they may well represent a lot of security. Gone... the moment a new version of the software no longer sees the transaction as being valid.
As far as I see it, if malleability can be fixed in such a way that older versions of the software still see immalleable transactions as valid transactions then, well
do it.