Going off the pooling mode feature map[0], it might be possible to mitigate that issue using transaction pooling, but not session pooling — which means a restricted feature set and cooperation from the application (which would just not call restricted features up).

  [0] http://www.pgbouncer.org/features.html#fn:2

Perhaps yes, would be worthwhile to benchmark an internal (to your runtime) conn pooler versus external only.

I'm using internal pools + pgbouncer but as I write this out I am beginning to wonder if that is even necessary.