The prevailing theory for why the brain uses spiking networks is that it is much more energy efficient to transmit "all-or-nothing" spikes versus propagating analog membrane potential across very large axonal trees. Contemporary machine learning is focused on rate-based neural networks with continuous activation levels representing the firing rate of the neurons. This makes these networks unable to measure the time difference between spikes arriving at a single neuron, an ability which is known to play a critical role in your auditory system for example. It is unknown how it is used in other parts of your brain. However, in recent years the concept of dendritic computation, defined as computation being done by the complex interaction of synaptic activations as they pass down a dendritic tree before reaching the neuron soma, has gained a lot of attention. If you do not create networks where time is a "first-class citizen" you will be totally unable to do this. Of course this might be more of an academic interest depending on your point of view.

The power efficiency argument from biology translates well to silicon when you want to build large structures. Here you cannot have 32-bit floats being passed around to thousands of target synapses, so you must make do with less.