No, that's not it entirely, or even mostly. Not so long ago a lot of Indexscript directories were hacked, and the main way they were found by the hackers was presumably the "powered by" link at the bottom. When you have a footprint like that it doesn't give you much time to respond to security threats.
Secondly, there's the issue of avoiding automated directory spammers, particularly when image captcha breaking is common. Anyone running a niche directory is likely to want to attract visitors interested in that niche, rather than just blanket submissions from lazy SEOs. It also means that when you create your own form field names it's easy to identify automated submissions.
Avoiding duplicate content is a distant third, because it shouldn't be an issue for well-run directories. But building a script from scratch does mean you're never tempted to cut corners and use the default text for any pages.