That would only be good for unique transactions, and for individual wallets.
If you have User 1 and 2 sending the same amount from Exchange A/online Wallet A to Exchange B/Online Wallet B, and only one transaction goes in the blockchain, whose is it?
And how long do you wait before re-sending the transaction if you don't spot it?
The more you wait, the greater the risk a User 3 will ask for the same transaction, which will just further mess things up, and it wouldn't be hard to exploit your input/output based "simple" transaction check to cause trouble.
A safer solution under the current protocol would be to spam the blockchain by including signature transactions: small extra amounts going to specific addresses known to the exchange, and that are unique (to the exchange) at any point in time. This will cause transaction dust of course, which is its own problem.
I'm not sure you understand how bitcoin works. The problem which precipitated this is not about different users requesting different transactions. It is about the
same transaction being "helpfully" modified to be standards compliant, but in the process changing the txid. However it is still the same transaction. The same funds going from the same inputs (albeit with modified scriptSigs) to the same outputs. It is easy to check whether a similar mutated transaction got on the chain or not.