It's possible to understand both exponential and limiting behavior at the same time. I work in an office full of scientists. Our team scrammed the workplace on March 10, 2020.

To the scientists, it was intuitively obvious that the curve could not surpass 100% of the population. An exponential curve with no turning point is almost always seen as a sure sign that something is wrong with your model. But we didn't have a clue as to the actual limit, and any putative limit below 100% would need a justification, which we didn't have, or some dramatic change to the fundamental conditions, which we couldn't guess.

The typical practice is to watch the curve for any sign of a departure from exponential behavior, and then say: "I told you so." ;-)

The first change may have been social isolation. In fact that was pretty much the only arrow in our quivers. The second change was the vaccine, which changed both the infection rate and the mortality rate, dramatically.