That's exactly the sort of test you get with the Selenium browser plugin: click "Record", do some things, verify the end state, click "Stop". You can then replay what is effectively an acceptance test. The problem (and it's a doozy) is that these tests are about as brittle as it gets: change basically anything in the markup and the test will fail. A good unit test will only ever touch a tiny area of the system, and therefore has a correspondingly tiny chance of failing whenever the system changes. And when it does fail because of changes to the rest of the system, it's usually for a good reason, like a changed argument list, not a bad reason like moving a button.

In short, these sorts of tests are super easy to create but become a massive friction at every level of the application since they depend on so much.