Testing only one thing will isolate that one thing and prove whether or not it works. That is the idea with unit testing. Nothing wrong with tests that test more than one thing, but that is generally referred to as integration testing. They both have merits, based on context.
To use an example, if your bedside lamp doesn’t turn on, and you replace the bulb and switch the extension cord, you don’t know which change fixed the issue. Should have done unit testing, and separated your concerns to isolate the problem.
Update: I read this article and linked articles and I gotta say, I’m shook: https://techbeacon.com/app-dev-testing/no-1-unit-testing-best-practice-stop-doing-it
There is substance here and it gets the mental juices flowing. But I reckon that it jibes with the original sentiment that we should be doing the test that context demands. I suppose I’d just append that to say that we need to get closer to knowing for sure the benefits of different testing on a system and less of a cross-your-fingers approach. Measurements/quantifications and all that good stuff.