Unless you specify an error, all growth can be approximated with exponentials. In fact, by your logic, even investors don't desire exponential growth. Why specifically would they want the growth of their investments to follow the rule that the derivative of the revenue is proportional to the revenue? Investors surely wouldn't mind factorial growth :) . It is just that metrics like CAGR are convenient and very rough approximations of the reality, designed to make the concept of growth intuitively year-on-year. In reality companies don't grow exponentially, we use exponential models to define company growth. The exponential model is fully arbitrary, with the k being as small as you please (linear growth is sometimes even defined by low CAGR numbers like 0.1%, etc.)
> Why specifically would they want the growth of their investments to follow the rule that the derivative of the revenue is proportional to the revenue?
Well, I think more precisely they want the growth to be at least exponential; they'd be happy with super-exponential growth (increasing, rather than constant, k over subsequent intervals.)
