You raised a good point about alert dialogs and it helped me refine my thoughts. Sometimes it's actually worth it to "reinvent" browser features. I don't know anyone who thinks that alert dialogs are good UX. So "reinventing the wheel" doesn't work here because it's too broad.
I found the concept I was looking for, and it's called "perceived affordances" vs. "false affordances." A perceived affordance is any sort of intuitive, visual clue that a user can perform an action. For example, text that is blue and underlined lets a user know it is a link that can be clicked. A false affordance is a perceived affordance that is not real. For example, a back button that does not do the intuitive function of taking you one screen back is a false affordance.
Some browser features are not used for a good reason. The Alert, Prompt, and Confirm popups for example block the whole browser -not just the current tab- because they're older than tabs.