I think that this is a reasonable suggestion, though checking to see if LTI authentication is enabled isn't as simple as checking if the authen_LTI.conf file is included. There are other ways to enable LTI authentication, such as by adding all of the configuration variables to the course.conf file for a single course.
I have started a discussion at https://github.com/openwebwork/webwork2/discussions/1794 about this feature request. You can add your thoughts there. If you feel comfortable implementing this then you can submit a pull request to the WeBWorK repository on GitHub.