I’d like to disable the TRUST authentication method for certain servers where modification of pg_hba.conf and restarting a service is fairly easy for a number of users.
I am aware that this would not make the server entirely secure but it would make it at least a bit more difficult to enter.
I'm not sure this is such a good idea. You may need the trust authentication method, for example if you forgot the superuser password. Otherwise, there's good chance you might use the ClientAuthentication hook to do what you want.
If you're an server admin you can disable the extension (editing shared_pre_load_libraries GUC), change password and then enable the extension again...
That would require a restart.
And maybe you can implement a simple way to enable/disable this hook inside the extension.