I think the process you're describing ("Design this service") is quite common and well established. I'm looking at the chapters in System Design Interview - every one after chapter 3 is titled like "Design a chat system", "Design Youtube", "Design Google Drive" etc. So it seems more like your expectations were off rather than the interviewers giving you something weird.
I think the process you're describing ("Design this service") is quite common and well established. I'm looking at the chapters in System Design Interview - every one after chapter 3 is titled like "Design a chat system", "Design Youtube", "Design Google Drive" etc. So it seems more like your expectations were off rather than the interviewers giving you something weird.