This is a great idea, but I think it's worth reconsidering the "first person to answer, handles it" logic. All the folks who didn't answer in time are now panicked with no idea what's going on.
Instead, you could make it so anyone who answers after the first person starts out muted and hears a message like: "Uncle Bob's on the line, press 1 to join the call or stay on the line to listen quietly." They could then choose whether or not to join in.
Just a thought! Great idea nonetheless — I'd buy it if I had a valid use case!
Great idea nonetheless though!