Is it bad to use add-on domains, or host multiple websites on a single cPanel? Will this affect search engine rankings? Because for example, when I search: site:maindomain.com I am able to view the directories of my other add-on domains in the search results.
You can ignore that by putting a blank index.html file into the main directory if there isn't a site in it. Unfortunately it's too late for that. Addon domains aren't bad, they're handy. But about your case, I don't know if it could hurt in terms of duplicate content (that's what you mean I guess), maybe try using a 301 redirect from that page to your homepage?