Its not a failure of culture, it's Capitalism.
Plenty of capitalists are happy running businesses at steady state. Some, even to wind down. (We tend to have nasty names for the latter.)
Growth at all costs is not a problem with our commercial culture at large nor with capitalism. It’s a convenient bogeyman for when we want to punt on a problem.
There are plenty of business owners who are happy to run at steady state---sole proprietors and family businesses, for example. These kinds of businesses can exist without capital per se, they can be financed with debt. But for businesses with investors, which is to say businesses backed by capital with the expectation that there will be a substantial return on the investment, growth is imperative.
So no, I don't believe there are plenty of capitalists happy to run a business at steady state, because one of the requirements of a capital investment is that the value of the investment grows, and the more rapidly, the better. A business owner may philosophically believe in capitalism, but that does not make them a capitalist in the active sense.
You've defined capitalism circularly to your argument. A steady-stage investor, whether a sole proprietor or outside investor in a business throwing off healthy dividends, is by definition not a capitalist by your book. Fine. Let's abandon the word for now.
The broader system of private ownership--the one we have in America. That doesn't require growth at all costs. Neither do outside investors. There are entire categories of outside investors who specialize in zero-growth or negative-growth companies. We can call it capitalism, as most people do, or private property or peanut malanga, the system and its mechanisms remain the same.
Growth-oriented investors need growth. And if you've spent your life around leveraged folk and venture capitalists, it may seem that's most of the capital in the world. But it's not. They're called alternative assets for a reason. The main universe of assets broadly accepts–in fact seeks-preservation of real value plus income.
Not so much a circular definition as a practical one. Technically an investor could invest only to get dividends or rent, but in today's world, in both the stock market and real estate, growth and appreciation dominate. Maybe this is a cultural preference that could be changed, but I think it's deeper than that: the growth imperative emerges from the competitive nature of capitalism itself, so that the system is inevitably and unavoidably growth-seeking. I hope you're right, and that a more essential asset preservation + income system can be sustained. But without significant wealth regulation, I have my doubts.