Even if you ignore all the neuromodulatory chemistry, much of the interesting processing happens at sub-threshold depolarizations, depending on millisecond-scale coincidence detection from synapses distributed through an enormous, and slow-conducting dendritic network. The simple electrical signal transmission model, where an input neuron causes reliable spiking in an output neuron, comes from skeletal muscle, which served as the model for synaptic transmission for decades, just because it was a lot easier to study than actual inter-neural synapses.
But even that doesn’t matter if we can’t map the inter-neuronal connections, and so far that’s only been done for the 300 neurons of the c elegans ganglia (i.e., not even a ‘real’ brain), after a decade of work. Nowhere close to mapping the neuroscientists’ favorite model, aplysia, which only has 20,000 neurons. Maybe statistics will wash out some of those details by the time you get to humans 10^11 neuron systems, but considering how badly current network models are for predicting even simple behaviors, I’m going to say more details matter than we will discover any time soon.