How meaningful is the benchmark for handling idle connections? Handling more is better, of course, but if the server melts down when 0.1% of them have any activity, maybe maximizing idle connections isn't the right place to expend optimization effort?
For us, the experiment (https://blog.mozilla.org/services/2018/10/03/upcoming-push-s...) with mostly idle clients was very helpful, since it flushed out problems with out load balancing layer and in the end gave us confidence that it, our app, and our persistence layer could safely handle many more connections.
If we had begun having problems once we started sending more push messages, we would have simply stopped using the new service (https://github.com/mozilla-services/megaphone) responsible for that until we worked through them.