This is important to introduce biases because it allows for the model to have adjustable thresholds values.
Considering for instance a neuron with a ReLU activation function, the fact that this neuron outputs in the flat region of its activation function or not may only depend on a scale invariant condition on its input vector, which is not true in the presence of a bias.
Hence we can see that the non linearity of biased neurons can extend further than that of unbiased ones, and that biased neurons may learn more objective criteria, like "this combination of my inputs is greater than 3" while unbiased neurons may only learn relative criteria, like "this first combination of my inputs is greater than this second one" which would remain unchanged if the whole input vector was multiplied by a positive factor.
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