A logistic curve is simpler than an exponential curve in the same way that crashing on Mercury unaided is simpler than landing on Mercury with retrorockets – not at all. It's the latter that assumes the rockets will actually fire.
It's not about simplicity. That's not what Occam's Razor says. It's about making the least amount of assumptions.
One thing that we see in many different aspects of the world is growth eventually plateauing. We don't see a whole lot that just keeps on exponentially growing. With that knowledge, a logistic curve (not logarithmic, my bad) is the one that most commonly occurs. That doesn't make it right, but it is more probable than exponential, which makes too many assumptions, and most of all invokes something similar to the gambler's fallacy.