The problem with ARM computers is that they, although rather power-saving, are not viable network devices. Their CPUs are too slow for serious file transfers.
I'm not so sure about that.
I don't think that the Pi Zero is something that you want to hook up a keyboard to. Instead, these kinds of computers are better suited to specific purposes. You might want to have it control some sensors in your home.
I saw a couple projects for an Arduino, which has far less power than a Pi Zero, where it was controlling sensors and lighting in a bathroom. When someone walked in at night, it would detect movement, then slowly fade in the lights. How many times have you woken up at night, stumbled into the bathroom, and then been blinded when you turned on the lights FULL BLAST? A few people have solved that with tiny computers, like the Pi Zero.
Sure, it's not a massive application, but it's still useful.
But there's no reason why you couldn't hook up a Wi-Fi module to the Pi Zero and have it communicate those tiny bits of data you want for running things like home automation. You don't need a huge amount of data transfer for it.
So while it's certainly not fit for some applications, it's still more than enough to run some.