You forgot to mention, crucially, that neurons in close proximity affect each other, which is just one of the things that makes modeling of more than a few neurons in time domain a complete non-starter. It all results in enormous systems of PDEs which we don't know how to solve yet at all. You could say that we do not have the right mathematical apparatus to model any such thing.
I don't follow that. What would prevent (perhaps quite slow) simulation of a larger system of such neurons? E.g. N-body problems are analytically beyond us, but can be simulated to arbitrary precision with certain trade-offs.
Time domain solutions do not exist for more than a dozen neurons. At least they did not when I took a computational neuroscience MOOC a couple of years ago. State of the art at the time was the nervous system of an earthworm. That is, if you consider what you actually need to do to simulate how potentials will change in the brain over time give a certain starting state and stimuli, the math gets so complicated (and awkward) so quickly that it's not really tractable with the mathematical (or simulation) apparatus we currently have to go beyond such trivial systems.
