The user pays a lightning invoice at the amount of 1 US dollar at the current BTC/USD price. The mint now has that amount of lightning held at the mint. The user now has an ecash token for a dollar pegged at that BTC/USD price. If the ecash token is not immediately sent, used, and redeemed for BTC. Then the fluctuations in BTC/USD price will mean either that either the mint will have a gain and when the $1 USD of ecash is redeemed for lightning, there will be lightning left over for the mint to keep, OR the mint will become insolvent and won’t have enough BTC to payout all the ecash receipts.

If the payment is immediately used avoiding the price fluctuations problem, what’s the point? Why not just settle in Lightning based on the BTC/USD price?

Once CBDCs are a thing, I think you can do what you describe above with CHDC instead of Lightning and you gain the privacy benefits of ecash. But I’m not getting what this enables. What am I missing? 

 Presumably, the mint shorts the BTC on an exchange and keeps the positive carry that bitcoin perpetuals normally have

though everything has a fee so the mint will need to be charging at least 30 basis points for them to not run at a loss