As with everything, it depends...
Do you want to sit in front of the Product Owner and say, with absolute confidence, that your API behaves correctly for authenticated AND non-authenticated users? When they "are you sure?", do you want to show them a bunch of tests which prove it? If so, your time has not been wasted. Your tests prove a requirement has been met.
What happens if someone accidentally removes the middleware declaration from the routes file, or removes your constructor? Will you have tests to catch this? You will if you test for authed and non-authed usage.
You've written them. They prove a requirement has been met. I'd say keep them in. :)
To give you an anecdote, I recently wrote an API which was protected by a "role" assigned to some users. My manual and automated tests showed this working fine locally. My PR went up to our build server and failed some automated tests. It turns out I had manually added the new role to my local DB during development. However, I had forgotten to create a seed file to add the new role. My permission-based tests caught that and I was very glad they did!