I think you have a very good practical understanding. Everything you say from "Here's the rub" and below is widely accepted
I think what you don't appreciate is that all the practical limitations of the BSM formula were also well-appreciated early on by just about everybody, including the inventors
. The model formula quickly morphed into just a convenient way to discuss market prices, via implied volatility. Everybody gets that.
So, you are beating a dead horse by pointing out these limitations.
The BSM formula is derived from a simplified model of the world
. It does offer general insights: indeed, enough to be worthy of a Nobel prize. It was Nobel prize-worthy, despite the limitations. Remember, we are talking about the economics prize here, which is often, IMO, more of an academic lifetime achievement award.
To really understand it conceptually, if that is your goal, that means mathematically
. To do that, you need to spend some time learning stochastic calculus and its connection with parabolic partial differential equations. Without that understanding, anything anybody says will sound like hand-waving.
Alternatively, if your goal is to critique it, don't bother. Trust me that the traders understanding and the academic finance understanding of the many limitations of the model are quite compatible and well-known.
Hope it helps.