There are much better ways to do this than using up what limited SIGHASH bits we have, and we already have other uses for SIGHASH bits that should be implemented.
In particular it has been proposed to extend the merkle tree of transactions down into the transactions themselves, which would allow you to easily provide compact proofs of the value of the transaction outputs that a transaction is spending.
tl;dr: Strong NACK on SIGHASH_WITHINPUTVALUE
You seem to suggest there is consensus about your opinion it should not be done, and that there are seriously-considered proposals to change the meaning of the merkle root. But, if you read the rest of this thread, there is a quite a bit of high-level support for this modification, as an "add-on" to any future hard forks. Of course, we're all happy to discuss alternatives, and what other uses there are for the other SIGHASH types, but you haven't mentioned what they are or where I can go read about it.
The all I see is gmaxwell: "I think the sighash with input value seems pretty inelegant." and Mike saying he likes the idea of doing something, lets talk more at the conference.
The seriously-considered proposals are the UTXO commitment proposals. As for other uses for SIGHASH bits, see IRC discussions about the need to be able to specify sets of txins and txouts being committed to. I also posted a quick idea myself for txout summation.
FWIW one of my main objections to this is that we really need general ways to prove fees paid by transactions for inflation fraud proofing, and short proofs of txout existence are very helpful to SPV nodes who are able to use them to check that transactions are valid - you're focusing on something very specific.
On the other hand, if we were to implement such a drastic/breaking change in the protocol as you suggest, to actually change what the merkle root means in the header, we'd have no problem simply "fixing" the existing hash types to include the output values, as that would equally break all existing parsing/verification code as changing the meaning of the merkle root. If your suggestion was implemented, we could remove the "wasted" SIGHASH_WITHINPUTVALUE bit and recover it for these other use cases you mention.
Additional merkle roots can be committed to in the coinbase txout; adding them is a soft-fork just like adding additional SIGHASH bits is. The best way to do this is to put the digest of the secondary merkle root in the last txout of the coinbase (with a P2Pool style 0-value OP_RETURN) so the proof can use a SHA256 midstate of the coinbase tx to keep the size independent of the size of the coinbase tx. It's at this point that a "v2" transaction format can be defined to fix all this stuff for once.
I'd be happy to pitch in on a BIP defining that transaction format, and we can do it in a way that leaves room to add the UTXO commitment digest when that is fleshed out as well.