I used to be a zoom guy when I started, but that lasted a few months, and stopped right after I 'got' the FA 50, both in the literal and figurative senses. Now I use primes only (not even mostly, but only).
(It's not the or even a better way, I want to stress here, just that it suits my style.)
First, I see better with primes, cos I already know how to frame the subject. This makes for better photos, for me.
I think the most important part of using primes, for me at least, is to accept I will not get some shots, because the 'wrong' lens is on at that moment. But I keep in mind that even if I have a super zoom, or a pair of 16-50 and 50-150 for quality maximum coverage, I will still miss some shots. And this is where the zen part comes in. Let them go, it's not possible to get every shot we want.
And the other key factor is, I can last longer when using primes. How so? When I use a zoom, the bulk, the weight and the zooming itself tires me out faster, so I get more uncomfortable and fatigued easily. It's both a physical and psychological thing, I guess.
Hope this throws some light on why and how some people use primes exclusively! Cheers!