I think you're missing the point of DISPLAY. It's there to point at an X server. If you have it set, you're telling programs that X is there. If you have PERL5OPT, about all you're telling programs is that you use perl, not that you're using perl for the current application. I think a better example would be ORACLE_HOME or DB2INSTANCE - if you've got these set, you're telling applications where to find Oracle, or that you're in a DB2 environment. Neither one may be working, but if I'm an application which relies on either Oracle or DB2 (perhaps with a fall-back), I'm going to read these to find out where to find Oracle or DB2. And, if they're set up incorrectly, I don't think it's unreasonable for me to fail with some error message complaining about these variables.

Same thing as DISPLAY. DISPLAY is there to set up X. If you're not using X, then you're misleading the applications that use X. Convention says that if DISPLAY is set, you may attempt to use it. If authentication fails, you then exit with an error message. This may mean that you set DISPLAY incorrectly (and wish a chance to set it properly), or that you shouldn't have DISPLAY set at all (and then you can unset it, and retry, assuming the application in question supports a non-GUI interface).