This creates a lot of confusion when project types like unit tests are impossible to find in the wizard. I tried switching the template to Desktop Templates and creating a project, hoping that it would remember my choice the next time I opened it, but it didn't.

There's no way to predict which template the user wants based on his installed Qt versions, but a combination of defaulting to Desktop the first time a fresh Creator is run and remembering the last template used the next time the wizard is opened would probably solve this problem.