In fact, for something as small as, say, cat, which has one executable and one man page, this may be so. But consider, say, KDE, which has a mountain of components, dependencies, and likes to stick them everywhere. Keeping track of it all would be tough, if not impossible. Package management makes it all easier. By letting a program maintain the information about the binaries, their configuration files, and everything else about them, you can identify which ones are installed, remove them easily or upgrade them readily, as well.
Installation becomes a snap.
You select what you want, and ask the system to take care of the dirty work for you. Unpack the program, ensure that there is space, place things in the right order, and set them up for you. Dependencies, or additional requirements for a software package, are also managed seamlessly by a good package manager. Management of installed packages is also greatly facilitated by a good package management system. It keeps a full list of software installed, which is useful to see if you have something installed.