You have an over-narrow concept of 'services'. A large part of 'service' wealth creation happens in management of supply chains (import/export, sales, marketing, logistics, right down to shelf stacking and warehouse workers) which scale alongside industrial demand, not population. Overseas manufacturers can't access markets at all without effectively paying service providers to help them distribute their goods. Walmart is, in a way, an exporter of market access services.

That's even before you consider service industries that create intellectual property which scale with global laziness and boredom, or the finance industry which provides services that scale with global economic activity, rather than local population.