You might as well ask why bother making subroutines, or why bother using OO, since the answers are essentially the same. To give you a real world example, at my work we have built a base class that automates the common pattern of show the form, check for errors, show the errors or process the input, and show a confirmation page. We can add new forms with all of that functionality by filling in a couple of methods (the validation profile and the processing for successful input). We also got a bunch of this for free by using CGI::Application::Plugin::ValidateRM
Usually, OO and modular code are not about reducing code size. They are about isolating pieces of the code from each other and gaining reuse. Using a module for your web app will help a lot with that.