ANNs don't yet model the structure of the brain but it seems plausible that they could do in the future as the result of some "convergent evolution".
ANNs have a fair model of individual neurons. Artificial and biological neurons do roughly the same thing when evaluated, but they are connected and trained very differently.
For me it's too much of a coincidence that the two most generally intelligent systems (ANNs and BNNs) are both "linear networks of activation functions".
We have not managed to build general intelligence from any other formalism, and neither has nature.
Viewing ANNs as a poor model of BNNs may be looking at the question backwards. You could say that BNNs are trying desperately hard to model the pure mathematics of ANNs within the confines of biochemistry. The fact that a biological neuron is not exactly a ReLU may say more about the limitations of biology rather than the limitations of ReLUs.