Good introduction to ergodicity! But terrible fulfillment of your promise that ergodicity says that the more the country's economy grows, the less the average resident earns.

Ergodicity is a very important concept when trying to characterize the behavior of large systems, and understanding that the economy is not ergotic at the level of individuals (for a variety of reasons, including that people are different, that lifespans are finite, and that civilization is not unchanging over time) is also good.

But it doesn't provide any predictions about what will happen vis a vis GDP; it only provides space for the possibility that the economy could grow while the typical resident does not see their earnings grow.