I think you're onto something with your motivation: most epidemiological models basically consider the infection/mortality/recovery rate to be fixed, or at most modifiable over many years by national investments in health. It seems that, before COVID-19, nobody had really thought that the trajectory of an ongoing pandemic could be changed, so I haven't seen any models which incorporate that.
But I think it's unfair to use scare-quotes around "models". The truth is, there is a tremendous amount of insight to be gained from those "models" (SIS, SIR, SEIR, etc.). I mean, your own proposed model is even just a small variation of one of the classical models, and you don't even show that it makes better long-term predictions, which is what you criticise in the other models.
Sorry, that was a long-winded way of basically saying: Great work, but don't discount the classic models entirely!
But, the differential equation models shown on the Wikipedia page have no policy/response variables, and basically assume an unintelligent, static null response. That was what was feared initially (early March), but of course fear drives behavior, so there's a closed-loop system here. That's my small variation and I think it's probably an important one.
Ironically, models without such complexities are often referred to as engineering or physics inspired - from the observation that human behavior is more complex and interdependent than the objects under consideration in physical systems. Natural scientists and engineers delving into social systems frequently fall prey to these issues.
In contrast, I've recently modeled the pandemic response as a feedback control system, where policy/public behavior affects infection rate, which affects policy. This is a classic feedback engineering problem. I'm able to vary suppression vs. mitigation along a continuous curve and look at the long-term course of the pandemic. Counterintuitively, the policy frontier (economic vs human damage) is concave and non-monotonic, and has three distinct regions. https://www.circuitlab.com/blog/2020/05/28/surprising-covid-...
We need engineering-driven long-term thinking, so that we can agree on an optimal strategy, before we choose individual tactics to implement that strategy.