why should I have things on my computer, taking up space, that I don’t want or need?
This is a fair question. My answer is that space on modern hard drives is so ridiculously inexpensive that the space itself is not a good enough reason to worry about a few extra files.
Things that might be worth worrying about are files that adversely affect the performance or security of your system. Both of these factors must be balanced against system stability when deciding whether or not to begin deleting files that are used by an application which has been dragged to the trash.
Applications do two things during installation and configuration. They create new files, and they modify existing files. When an application creates a new file, it is probably safe to delete when you trash the application. When an application modifies an existing file, all bets are off. Completely removing all traces of an application is a very difficult task if you presume that no damage to the system is acceptable, and I think that is a fair expectation.
Hidden files are hidden for a specific reason, which is to make them difficult or impossible to be inadvertently or improperly deleted. In many years of working with several flavors of Unix, Windows and OS X, I have seen only a handful of situations where hidden remnants of an application caused instability or insecurity in the system. Ironically, some of the most serious problems were in-place upgrades from OS 9 to OS X.
IMHO, unless there is a readily identifiable performance or security issue caused by remnants of trashed applications, hunting down and deleting those remnants creates more risk of system damage than leaving them in place until the next clean installation.