As far as critiquing models is concerned, clearly, capturing a complex spatially distributed process in a simple localized model is only ever going to produce a rough approximation. Those logistic fits, specifically, are motivated by a description of epidemics on the basis of a localized model (we used to call these "lumped parameter models") which result in a fairly simple (set of) ordinary differential equation(s), and, in their simplest case, the logistic function as a solution. All of these, very much including those SIR/SEIR/… models, suffer from the assumption of spatially uniform parameters.
In contrast, in particular in the US right now, we have widely varying population densities, chaotic testing, and wildly varying levels of compliance with social distancing rules. While I would therefore expect individual hot spots to be more easily described with localized models, that's near-impossible for the US as a whole.
I wish people would spend more effort on much more realistic approaches such as Wolfram's agent-based networks. Yes, those are enormously computation-intensive (and data-hungry), but models of that nature could at least clarify some crucial questions that are poorly understood at this point. Take just the question of the efficacy of social distancing, which is clearly hugely important: Current approaches take an enormous economic toll, and at some point the question needs to be asked (well, it's being asked right now) if and how these rules should be relaxed. Yet, to be perfectly frank, there is basically no real understanding, none at all, of what the effects of those social distancing rules w.r.t. cases and deaths could be. Sure, people babble about how "social distancing works", and it probably does, to some degree, but there is no quantitative understanding. Agent-based networks could provide some insight, but that will require a massive effort. Are there any groups who are doing such simulations?
