That's what the math says should happen. It's not what the measurements say. If you look on http://91-divoc.com/pages/covid-visualization/ you will see country after country goes linear. The USA for example had 30k new infections most day for a remarkable 2 months.
I have no idea what causes it. It could be measurement error (that's what I first put it down to in the USA). But if it is it damned hard to explain why it has happened over and over again. Russia has been sitting on 9k new cases per day for 2 months now. The UK went through a period of 5k new cases per day for a month.
It's not a universal, or even the most common pattern. But it happens enough to make the statement "the measures of new covoid 19 cases always change exponentially" wrong enough to be effectively useless as a prediction of where things will head.