But isn't this just a more abstract example of the 'circular explanations' thing that OP mentioned? The reason why we need compound interest on our savings accounts instead of just being able to put away some money every year is a product of having to counteract inflation, which is the result of policies trying to induce growth by making saving less appealing than putting the money into more companies making more things for more profit. We need infinite growth because everything around us is designed to expect infinite growth. But what happens as we start running out of headroom? Is there really no other way at all?

We are going to find out. See Limits to Growth.