Clinton, I think the key to a useful test is that you are testing something that you want to ensure doesn't break without you knowing about it. In the lesson, we look at testing that a string of classnames contains a specific substring to ensure that our icons will be rendered correctly; this is not
this.props.string = string but rather
this.props.string.includes('substring'). In this situation, the value comes in knowing that our icons are rendering correctly - and we don't have to manually check this in the browser any time we make a change to the Icon component.
There are hundreds of other use cases for this, but the principle is that we...
1) found something that is important - that we don't want to break accidentally when we refactor or add features in the future (in this case, icons are rendering by type)
2) figure out what piece of our code will ensure that #1 is working (in this case, the right substring exists in the rendered className prop)
3) write a test with #2; generally I've found it helpful if the test isn't tied to a specific DOM structure or lots of React specific things, as you pointed out.
I've found generic tests like this to be very useful :)