you've finally provided the answer I've been looking for here at ET: Economic growth is needed because otherwise capitalism will fail as a construct.

In my role of providing Socratic questions: Is economic growth the petrol of the captialism machine? (And what is then the exhaust?)

Similarly, is the Steady State Economy as you describe automatically different from a capitalism economy?

Growth is promoted by economists because they are paid by the financial industry (some indirectly). In a capitalist system people expect to get back more money than they put in when they invest. In truth there are only three ways this can happen: population growth, productivity growth and inflation. So economists need to promote growth otherwise capitalism wouldn't work.

Aren't we in a way putting the cart before the horses here?

Capitalism may require growth, but it doesn't cause it. Where does growth come from, and where does Capitalism come from?

I can't pretend to even begin to understand the political economy of Antiquity, but the conventional wisdom about the origins of capitalism seems to be that after the 14th Century plague in Europe, the European economy embarked on a bout of growth that is not yet over. That's over 6 centuries of growth. Wikipedia paints a slightly different picture with up to 70 years of collapse and stagnation up to 1500 followed by growth:

Europe had been overpopulated before the plague, and a reduction of 30% to 50% of the population could have resulted in higher wages and more available land and food for peasants because of less competition for resources. However, for reasons that are still debated, population levels in fact continued to decline until around 1420 and did not begin to rise again until 1470, so the initial Black Death event on its own does not entirely provide a satisfactory explanation to this extended period of decline in prosperity.

Capitalism is the economic system of the early modern bout of economic growth. It is this economic growth that allows the birth of the modern financial system [for instance, loans on interest became acceptable after having been condemned by the Church throughout the Middle Ages]. This economic growth is fuelled by cultural and technical innovation, but also by the exploitation of natural resources in the newly "discovered" America and by the opening of new trade routes to Africa and Asia.  Once the financial system gets going, and with a constant influx of gold and silver from South America, it becomes the driving force of political and economic change and the growth which originated the new system becomes a necessity to perpetuate it.

Nothing is 'mere'. — Richard P. Feynman