They are not the most productive way to get end to end automated test coverage.
Besides that, sometimes code just doesn’t change (say a basic math library). Then you’re mostly testing your compiler, which is useful but an intentional approach would be better.
Unit tests do come in handy when building a maths library.l or similar. Not in terms of catching a regression, but to help build it in the first place. One of the few places where TDD might actually be helpful.
The big drawback is I have to check all these tests/demos manually (across browsers and devices) before releasing a new version of the library into the wild. Automating that process is on my list of Things To Do - if anyone has suggestions/insights into current tooling/testing suites that could help me then I'm very willing to listen and learn!