Is it a promise to reject any block contains a different transaction with the same inputs? That might leave the miner off the real chain forever no? But otherwise what does it matter? They'll mine the tx unless another gets in first? Not much help really.
its not a promise to reject, but a promise not to mine a conflicting transaction. and to include your transaction in a mined block (so even if a block is orphaned due to other reasons, the transaction will still be included later)
so if you got a signed reply from 40-50% of the hashpower - you can be quite safe that a competing transaction won't end up in the longest blockchain.
it's not 100% safe, but it's a good indicator.
But i think it has the potential to flood the network when there are a lot of transactions.maybe there should be a way to consolidate miner sigs. so if a client sees 2 verifications it will send out 1 packet with both sigs, so after a while you will have only 1 confirmed transaction being flooded in the network with a long list of sigs. and maybe add a timeout - you can only send/propogate a certain signed transaction once every 2 seconds - you will have more chances hearing new sigs in that time.