There is no One True Way© to make an SVG icon system. The only thing that SVG icon systems have in common is that, somehow, some way, SVG is used to show that icon. I gotta find some time to write up a post that goes into all the possibilities there.
One thing different systems tend to share is some kind of build process to turn a folder full of SVG files into a more programmatically digestible format. For example, gulp-svg-sprite takes your folder of SVGs and creates a SVG sprite (chunk of
<symbol>s) to use in that type of SVG icon system. Grunticon processes your folder of SVGs into a CSS file, and is capable of enhancing them into inline SVG. Gallagher's script creates React components out of them, and like he said, that's great for delivery to different targets as well as performance optimization, like code splitting.
This speaks to the versatility of SVG. It's just markup, so it's easy to work with.