The setup is kind of a kind of a logical fallacy here. More people are using Debian and RPM based distributions than Arch Linux. That being said:
Arch Linux has the AUR because at the time it was developed, the standards for distributing software on Linux were either RPM or DEB repositories. AUR was a necessity because one could get software on those distributions from the official vendor, but nobody was supporting Arch Linux. So it was a stopgap, an equalizer for one outlier platform.
It's hardly the first such repository: FreeBSD ports and NetBSD pkgsrc predate the AUR by over a decade. Slackpkg predates AUR by a couple of years as well, though possibly not slapt-get. Gentoo has portage. Anyway, they took an idea that was already well-established, and catered it to a distribution that had fewer software options than major distributions.
These days it's still the same scenario: a placeholder, to equalize what's available for Arch Linux users versus other distributions.
People use Arch because it is a rolling release with a well-documented wiki. AUR is a nice perk, but hardly the main reason that people are using Arch Linux, given that other similar systems have existed for older distributions and operating systems for longer.