Ohhh, I understand. Long day. I got that backwards, I thought there was a server-side option I wasn't aware of. So you don't have a dedicated server with PgBouncer on it, you just move the pooler to where the requests originates from. I think this might be problematic in a highly elastic/distributed architecture but would work if you have a beefy dedicated application instance.
Correct, you'd have to instruct your pools to resize as machines are added and removed. We haven't had to do that so far, as we're not that dramatically elastic.