If you do have a large number of clients, PgBouncer only means you have a single shared pool of connections rather than each replica having its own smaller pool

If you do have a large number of clients, PgBouncer only means you have a single shared pool of connections rather than each replica having its own smaller pool. You already have a load-balancer for the web clients, so the latter is maybe fine. Of course this doesn't work if you have more replicas than available DB connections.