Your intuition here is basically what's formalized by Piketty in "Capital in the 21st Century": that the rate of growth of capital exceeds the rate of economic growth.

What's interesting is that while intuitively this makes sense (for the reasons you gave), the implication (that the rich get richer and inequality grows) is the opposite of what was hypothized by Kuznets (https://en.wikipedia.org/wiki/Kuznets_curve); the latter hypothesis, to my limited understanding (as a non-economist), is fairly mainstream, and has influenced plenty of politics and public policy.