My guess is the non-uniform nature of the graph of human contacts, which is probably made up of several densely-connected clusters each with relatively weaker links to other clusters.

E.g. let’s say there is an office where everyone works in person and a bar with a group of regular customers. If someone in the office gets Covid, everyone in there has some decent chance of getting it. Similarly, if a bar regular gets Covid, each of the others has a decent chance to get it. But if only one person who works at the office is also a regular at the bar, then for the infection to hop from one cluster to the other, that person needs to get it from the initial outbreak, and they need to continue going into the office during their infectious period, and folks need to catch it from them, none of which is certain.

So, my guess is that after enough of these clusters get seeded to start a wave, “R” is initially high, but R decreases massively once enough of the infected clusters are saturated, possibly low enough to make the growth visibly non-exponential, even if the entire population infected rate is nowhere near the point where growth rate would decline in a simple logistic model.