That's true. However ...
> ... the circulation generated by the wings ...
You haven't explained why there is "circulation generated by the wings", you have just stated that there is.
Note, if you take the full flow over the wings and subtract the vector field that is the undisturbed average flow then you are left with a circulation. The two are effectively equivalent, so "explaining" by saying that there is "a circulation" is basically saying that the air flows faster over the top and slower underneath.
It's a non-explanation.
I do have an explanation as to why the air flows faster over the top, but this discussion is too small to contain it.
PS: I agree that all the modelling and equations work very well, and from that point of view its "well understood". However, the discussion here shows that for many people, even those who are technically capable, it is not "well understood".