I started a react component library project that has been going for 4 years now and gets about 40k downloads a month. If it wasn't for my test suite, things would have been a giant mess long ago and I probably would have abandoned it. I can't think of doing a react project without a test suite because over time, any dependencies you have (including on react) will end up breaking things in ways that you don't know. Wi…
I have yet to see a good frontend test, but I'm waiting to be enlightened. For the most part, it just seems to be things like "if they click this button, make sure this div is gone." That smells like a test double to me.
Some are simple (although very few are as simple as your example) and some are complex, depending on the portion of the app being tested. Some are basically integration tests for components/widgets, where it runs it in isolation to test the inputs and outputs. Others are more like traditional unit tests where it's purely testing business logic, API and model interactions (mocked), form validation logic, etc.
Unless you're talking about very simple client apps, there's always stuff that can be tested that will provide significant business value by preventing bugs and broken code from getting to end users