It sounds like a super fun question. I'm almost tempted to start thinking about it even though I'm not interviewing for anything.
Given how many features AWS alone ships every year, I'm sure Amazon is very familiar with prioritizing features and building MVPs. But you're interviewing for a software engineering position (I assume) and the question is explicitly about design, so project planning is off topic here. It's fine to mention it in passing, but the meat of the answer should be about the "initial technical approach" that you mention.
Your comment suggests that, due to your consulting experience, you flat out refused to draft an initial technical approach on the spot. That may be wise is other situations, but you aren't here as a consultant. Amazon isn't going to start implementing 1-hour delivery based on your plans. They're asking this question to see you think and work your way through a complex problem.
Additionally, your answer is so vague that it could apply to almost any question ("How to do X?" "Gather stakeholders and come up with an initial technical approach").
Given how many features AWS alone ships every year, I'm sure Amazon is very familiar with prioritizing features and building MVPs. But you're interviewing for a software engineering position (I assume) and the question is explicitly about design, so project planning is off topic here. It's fine to mention it in passing, but the meat of the answer should be about the "initial technical approach" that you mention.
Your comment suggests that, due to your consulting experience, you flat out refused to draft an initial technical approach on the spot. That may be wise is other situations, but you aren't here as a consultant. Amazon isn't going to start implementing 1-hour delivery based on your plans. They're asking this question to see you think and work your way through a complex problem.
Additionally, your answer is so vague that it could apply to almost any question ("How to do X?" "Gather stakeholders and come up with an initial technical approach").