It's been noticed before that inheritance is often not the best way to handle code reuse, but Java and Struts don't give you much choice (if you want a reasonably simple API). In any case, spreading your code out over many classes that are all somehow related, even disregarding code reuse issues, makes the code hard to understand and adapt IMHO.
I can see some potential in using Class::Prototyped (and hence, CGI::Prototype) in that regard, but I would have to try it "in the wild" to see if it really holds up.
Right now, I like the fact that you can just group a bunch of related runmodes into one CGI::Application subclass: it makes their relationship explicit and you can make a shared base class to for bigger applications if you need that.
updated: fixed typo