I expect high fees to become a problem long before 1 satoshi becomes too large to be the smallest unit.
Agreed. I suppose it depends on where you see Lightning Network or any other potential second layer or off chain solutions ending up. We could reach a point where the vast majority of bitcoin transactions take place on Lightning, with people keeping their channels open pretty much permanently. The only time you would be paying fees on the main chain would be if you needed to close your channel for whatever reason, or if you wanted to transact a large amount and have the added security of it being immediately broadcast to the chain, in which case paying fees of tens of dollars on movements of millions or dollars is probably acceptable.
Or, as ETF says, it could be that nodes and miners start accepting transactions with fees of less than 1 sat/byte, you just round the fee you are going to pay to the nearest whole satoshi.