I guess that’s very dependent of what kind of framework you’re using. The only PostgreSQL-driver I’ve seen that does not have connection pooling built-in is the PHP one (since PHP’s runtime model does not work in a way where that would be easily possible).
Local connection pooling only goes a very small way to mitigate this issue. If you have enough servers hitting PG, you're going to need to add in something like PgBouncer sooner or later.
It's still fairly easy to hit problems even when you're using an application level connection pool, simply because it's so damn easy to scale up application nodes.
