In my opinion, it is unlikely that everyday transactions will predominantly occur on-chain. Most on-chain transactions will likely be conducted by large institutions that will contribute to second layer solutions.
how about this. they invent this card that you can use to conduct purchases and other similar transactions. the company backing up the card has centralized servers. so it works really fast has high transactions per second. no maximum blocksize or anything like that. your card is backed up by bitcoin you let them hold for you. when you use your debit card to buy something, it's not going to appear on the blockchain, the company will just adjust your "bitcoin balance" with them.