If the inputs to my transaction have been long confirmed I can be reasonably safe in assuming that the transaction hash does not change anymore. It's true that I have to be careful not to build on top of transactions that use legacy references to transactions that are unconfirmed or have few confirmations, however that does not invalidate the utility of the normalized transaction IDs.
I remember reading about the SIGHASH proposal somewhere. It feels really hackish to me: It is a substantial change to the way signatures are verified, I cannot really see how this is a softfork if clients that did not update are unable to verify transactions using that SIGHASH Flag and it is adding more data (the normalized hash) to the script, which has to be stored as part of the transaction. It may be true that a node observing changes in the input transactions of a transaction using this flag could fix the problem, however it requires the node's intervention.
Compare that to the simple and clean solution in the proposal, which does not add extra data to be stored, keeps the OP_*SIG* semantics as they are and where once you sign a transaction it does not have to be monitored or changed in order to be valid.
There certainly are merits using the SIGHASH approach in the short term (it does not require a hard fork), however I think the normalized transaction ID is a cleaner and simpler long-term solution, even though it requires a hard-fork.