I would imagine the relay operates the mint and since lightning is used to get in/out your client could just use lightning to buy the exact amount of ecash needed for a stamp and then use that? Probably still prohibitively expensive with lightning fees for one stamp but maybe you could just round up to whatever makes sense whenever your balance is too low. 

 Sure, but the mint can still issue more tokens than it has in reserve. 

 Yeah I don't see it as functionally different than you loading an account somewhere with credits, or a custodial wallet. I think it might be useful as a formalized way for people to spin up an account system within their app/service with lightning in/out and some privacy internally, but still just as risky as holding funds on anywhere else custodially.