It's partly just due to historical differences, but partly because different distributions are geared toward different kinds of users. Red Hat and Debian are aimed mainly at business environments that need tried-and-true, stable software; Ubuntu is aimed at people who want the latest-and-greatest versions of everything with a minimum of fuss; Arch and Gentoo are aimed at experts who want to get their hands dirty and fine-tune their system.
The role of a Linux distribution is system integration: bringing together all the parts that make up a system (kernel, libraries, programs), configuring them to work together, performing stability testing, and providing an installer and an update system for users. This also involves developing additional, supporting software, such as the installer and the package system.
The way the system is put together (i.e. integrated) depends on the needs of the people who will be using it, so you get differences between the distributions. Gentoo developed Portage to make it easy for enthusiasts to recompile their whole system with customized build options; Red Hat developed kpatch to allow administrators to apply kernel security patches without having to reboot their mission-critical servers.
A distribution's package system is just a part of its system integration. So is the configuration for how system services like daemons are started, as well as configuration for other things like networking and security policy.