THis is the issue, until its settled in the chain, then you are down to trusting the 2nd layer.
Anything offchain has a whole bunch of issues that are either naively or deliberately obscured by the fact that it _eventually_ writes to the blockchain. The exchanges that offer instant settlement are circumventing trust by doing the settlement for you. You get speed, but not security that they have done what they have said they have.
This is just untrue. If someone cheats in lightning, and you demonstrate they cheated as you describe, then you get all of the locked BTC as a reward. This is on layer 1. Essentially you can easily prove your nonce was signed more recently.
Well, to be fair to OP: small business and retailers are also not getting "real" money when they accept payment via credit cards from Visa/MasterCard.
To be honest I think the issue here is not due to speed of settlement, but layer-2 is not an acceptable substitute because it does not allow reversability. For the merchants it's good that they are getting the money right away, but most consumers will not dare to pay anything via layer-2 networks simply because they won't have any recourse in case they want to undo the transaction.
You can implement reverseability with a credit system, such as Visa/Mastercard. It should not be implemented in base layer or layer-2. It is basically an escrow system.
So now you are proposing to build yet-another piece to an already complex system just so we can justify the existence of your beloved blockchain in the first place.
How long it's going to take you to realize that even if we built everything you are asking for, we are STILL going to end up with a system that is not as capital-efficient as the status quo?