The main reason assertions are not used is because they are not enabled by default. Therefore if you have a condition that is important enough to require an assertion you can’t rely on assertions being enabled to get the job done.
As other answers have correctly stated they’re designed for development-time testing and debugging because they cost nothing if assertions are disabled in production. I think it’s better to create explicit tests in your testing framework (e.g. a unit test for edge conditions) than rely on someone enabling assertions while testing.
However a good example I’ve seen for using assertions is checking private method arguments. Since you control the access to those methods you can check that your own class is using the method correctly while your public methods use more reliable argument checking techniques (annotations, if statements, 3rd-party libraries, etc). That way even if assertions are disabled your method should be protected but developers looking at the source code can see the preconditions for your method and turn assertions on for an extra safety net when working on that class.