With a statement like that, you're going against decades of experience which says polling doesn't scale. Constant connection setup and teardown is incredibly expensive.

RAM is cheap.

Push can scale. Ask Urban Airship. It is hard though and while polling is generally easier it has its own set of scaling problems.

Really? So there are no large-scale implementations of push-notification systems? Is there some detail I'm missing here?

The apple iOS push service would like to disagree.

Care to elaborate?

Server has to keep tabs on all clients, rather than being polled.