Based vs native rollups

Who should put a rollup's transactions in order, and who should check that its results are right? Ethereum researchers and rollup builders have argued over two answers: let Ethereum's own block proposers do the sequencing (based rollups), or let Ethereum's own execution do the checking through a built-in tool (native rollups, EIP-8079). Underneath sits a bigger question, how much of a layer 2 Ethereum should take on, and the people who build layer 2s have a say in it. Every quote is the speaker's own words in their order, with the ums and stumbles taken out; the original captions are one tap away.