Now if we (a node) see a system compromise, we require the SHA256(tx) value to be less than 1/1000000 * 256 bit value, we can be relatively confident the issuing wallet has done a certain amount of pow on that tx for it to be issued.
Why?
This is an emergency brake that bitcoin node operators could optionally enable if there was a system wide compromise. It gives bitcoin owners time to issue their own tx with a local PoW to move their funds to a QC safe or uncompromised signature system.
Yes each wallet would need an option to 'create a tx with PoW' but it seems this would distribute the work to the wallets/clients so a system wide attack vector is reduced.
Besides the change you mentioned, one more (and non-trivial) change is required - you see, block (header)s have a field for nonce, so the miners just keep increasing it until the SHA256(block) is less than whatever the target is.
But in a bitcoin
transaction field, no such field exists for a nonce. That means when you SHA256 a transaction, there will only be one possible value, unless someone adds a new field by using a fork.
The current fields of a Bitcoin transaction - as you can see, there are no "reserved" fields that can be taken advantage of to implement this procedure.