I expect on-chain transactions will eventually be extremely high-value, between major players and institutions willing to pay the fees, while the daily transactions will be on sidechains/other layers.
I'm not sure the fees will actually change a whole lot if denominated in BTC. I just expect that when 1 BTC is worth a lot more than it is now in fiat, people won't be paying for their coffee on-chain (assuming inflation doesn't do crazy things to the price of a cup of coffee!).
So just like the current financial system where the real transactions are between the fed and the banks while everyone else you me and him are just fiddling with numbers in a mainframe table.
I'm not sure the fees will actually change a whole lot if denominated in BTC. I just expect that when 1 BTC is worth a lot more than it is now in fiat, people won't be paying for their coffee on-chain (assuming inflation doesn't do crazy things to the price of a cup of coffee!).