10 minutes to deploy to production should be fine, but rapid iteration shouldn't be happening in production. It sounds more like the complaint is related to running a similar setup in dev, and taking 10 minutes to see changes during development (which is understandably too long).
Yep, that's what I meant. I have no choice but to run a local k8s cluster or else I can't test.
and then we're back to the original statement, if you're rapidly iterating hot fixes you have serious problems and likely doing it wrong.