The main reason why this isn't very feasable at the moment is due to tx id malleability (as the ECDSA signature is included in the tx id and the same tx can be signed with a different valid signature because ECDSA approach used by pretty much all Bitcoin wallets includes a "random" number).
I see. So if I get it right, this could lead to a double spend, by creating two similar (inputs, outputs # of coins) transactions with separate txids?
No. That can't happen. Only one of the transactions can be added to the blockchain.
The danger is that a maliciously malleated transaction (and not the one you created) will be confirmed, meaning that the txid won't be as you expected.
In more esoteric uses of bitcoin it is sometimes necessary to create and presign transactions which spend from transactions that have not yet been broadcast. This is known as chaining.
In such cases the txid of transactions appearing earlier in the chain must be guaranteed (ie unalterable). If a txid is altered all successive transactions in the chain will fail (because they will refer to outputs from transactions with txids that do not exist).