Basically, the AUR works by downloading source code and running a build script that builds the app specifically for an Arch system, right? So why isn’t there an equivalent that works on most or all distros? Almost every time, compiling a Linux app is just running the commands that the developer tells you to, and for the uncommon times there are distro-specific differences, they’re usually listed in the README. For many userspace apps, even building across different processor architectures requires little to no change in the commands required as long as there’s a platform specific compiler. Why isn’t there a cross-distro system that can download source code and run a build script while knowing what distro-specific commands to use based on the developer’s instructions? Heck, compiling an app on the system you plan on running it on can unlock a little more performance by taking advantage of compiler optimizations for that specific processor, and it doesn’t take that long on a reasonably modern computer anyway, so why isn’t there an incentive to do it more often?
People have tried and failed this concept for decades. It’s not a new idea, but it’s an incredibly large and complicated problem to solve, not only because package names and versions differ from distro to distro, or distro version to distro version, but the contents of the packages and what they support and are compiled with differ too.
In reality it’s not possible to get perfect, but with an absurd amount of effort a subset of support could be made. Your program just wouldn’t be able to have the same guaranteed feature set across distributions.