I don’t believe the setup is a fallacy, the AUR is one of the main reasons I use Arch. Sure, other distros may have similar systems in place, but the number of packages available on these systems just doesn’t compare. I did a brief amount of research, according to the FreeBSD manual, there are “over 30,000” ports available. In comparison, there are over 90,000 packages available on the AUR, and all of those are in addition to the ~13,000 packages in the official Arch repositories. If I want to obtain a piece of software, even if it isn’t in the arch repos, odds are, someone has already gone through the trouble of figuring out how to build/package it, and has added the PKGBUILD to the AUR.
This way of doing things is so much more elegant compared to how things are done on Debian or Red Hat-derived distros, where the solution to the problem of a piece of software not being in the official repos is to either (1) scour the internet and try to find if the developer maintains a repo for your distro, (2) look to see if a third party has packaged the software for your distro, and hope and pray that they maintain it, or (3), compile the package yourself, after manually hunting down all the various libraries the application needs, determining what they’re packaged as for your particular distro. The third solution doesn’t handle updates at all, unless the application’s developer has built-in an update checker into it.
Things are getting better as snaps and flatpaks gain popularity, but both of those systems have lots of issues of their own, and arguably aren’t anywhere near as good as a proper native package for your distro. Flatpaks don’t really work for CLI tools. Snaps are stupidly slow. Both snaps and flatpaks still struggle with theming. Applications installed with either take up way more space than their natively-packaged equivalents.