" and over half-a-dozen different major ways to install software such as the Debian Package Management System (DPKG), Red Hat Package Manager (RPM), Pacman, Zypper, and all too many others. "
There has also been CPIO, TAR, ZIP, RAR and others.. but nowadays it isn't uncommon for a single tool to be able to handle most archive formats, since they are just variants of the same conceptual thing. In the same way, package files are just variations of each other, so there is little technical reason why package manages can't read each other's formats, at which case it becomes more of just a user interface difference. Ideally, they could also use the same system database format(s), so you could use them interchangeable based on personal preference the same way someone uses the text editor of choice to edit the same files (but we're not quiet there yet).
Perhaps what's really needed is a non-profit organization who's goal is to help unite various distros with common APIs, without preference to any particular distro. If being a member of such an organization can provide additional developers (or direct funding), it might encourage them to be less fragmented, or eventually merge distros once the differences become trivial.