If I understand DoorDash's corporate structure, the founders have dual-class stock and voting control, so board could not remove them.

If the CEO is taking responsibility upon himself for leading his company in such a poor way he has to fire large swaths of people then he should quit. He's the CHIEF, the buck stops with him. What, is he going to keep his job and then just be a better CEO next time? He gets to make a hundred million dollar mistake and keep his job?

I've seen peers fired for much less.

The real answer is he doesn't take responsibility for anything other than doing his job exactly as expected and prioritizing short term profits for stakeholders.

Either quit, because you're a bad CEO, or do away with this "I'm taking responsibility" facade. Just be upfront with it. "I fired you to make a quick buck." I can at least respect the honesty there.