It would really be an insurance that if the chain confirmed a block containing a transaction spending the same inputs in a different way then the miner would pay the outputs himself instead.
I don't care for this twist myself. Funding the insurance would be complicated.
Rather than getting dinged because some net split resulted in you signing off on the wrong half of a double-spend, I would prefer the motivation to be to get a reward for including the transaction as promised,
But where's the incentive for a miner to do this?
Offer an extra tx fee for a miner who includes the transaction in a block after making a signed promise.
If you take 1 BTC and create two transactions, both spending it to different addresses, then send out both transactions simultaneously
The classic double-spend. The miner can wait a few seconds before making the promise to ensure there are no conflicts; and the recipient can watch for it as well. This will catch 90% of such attempts.
The rare exception will be where the network is severely split and the double-spender is able to exploit it to his advantage. Someone selling a cup of coffee won't be worried about such cases, but a business subject to fraud - a wallet service for example - could simply wait until they has signed promises from 75% of the network before accepting the transaction.
But how do you know something represents 40-50% of the hashpower? AFAIK, the only way of knowing is solving blocks.
Each time a miner signs a block they include a copy of a pubkey. The merchant gets the last 1000 pubkeys from the blockchain. If they want 75% of hashpower signing off, they wait until they have 750 signatures (or fewer: many of the blocks will have the same pubkey since most blocks are solved by a handful of pools; a pool which solved 150 of the last 100 blocks only needs to make the signed promise once).
It doesn't prove that it's approved by 75% of hashpower online
right now, but 75% of the hashpower for the last 1000 blocks.