Hi Gregory,

In particular not covering the ID allows for transaction replay which
can result in monetary losses far more severe than any possible
mishandling of malleability could result in. Byzantine attackers can
costlessly replay your old transactions any time anyone reuses an
address, even accidentally (which cannot be easily prevented since
they can race).

With the SIGHASH_WITHOUT_PREV_VALUE flag, signatures have to explicitly specify that they are to be signed without the previous UTXO's value/amount. This means that, at worst, replay attacks can send the money to the same place it was sent before (which in many cases is likely not be a loss of funds), and only if the amount sent to the reused address is the exact same as it was before. I don't think this is worse than an attacker being able to mutate their transaction and extort a merchant who accepts zero-conf transactions. Anyway, not signing the input ID wouldn't exactly be the norm, there would be a defined set of flags for standard use cases. Not signing the input TXID would only be used in specialized cases, such as setting up micropayment channels. 
 
There are no free lunches;  the proposal linked to there is itself a
game of wack-a-mole with assorted masking flags;

I agree that it is also a bit of wac-a-mole, but the defined space of issues is possibly more limited here. There are only X number of things that can be signed/not signed in a transaction, and the 'Build your own nHashType' proposal enables you to fully specify which of those are being signed. If you don't want to get burned by not fully signing your transactions, then don't use the non-standard sighash flags.

many of which we have
no notion of if they're useful for any particular application(s);

A few of the flags, indeed, may not ever be useful. But we can't predict the future, and I think it's better to build in a more flexible solution now than to wish we had more flexible nHashTypes later.

To the original point of this thread, hopefully the suggested proposal won't be necessary as wallets will upgrade to use version 3 transactions and the rules associated with them over time. 

Best,
Stephen