I sort of like the sentiment but this sort of interview, at least for me, would feel a bit too personal. Look I'm not your friend so let's not pretend that's what this or you just really want to get to know me. No. You just want to know if I can do the job so just get me to do a task which meaningfully reflects what I'd be doing day-to-day then ask me questions about it.
Do you not try to be friends with your colleagues? You spend about a third of your life at work, it seems to me that you should try to make it as enjoyable as possible.
In some ways, I find it's more enjoyable to not be friends with my colleagues; to keep my personal life and work life as widely separated as is feasible.