Why not just use a package manager? If the one in your distro sucks, find a better distro. (Arch Linux would be a good example.) The rule of thumb with OSes and implementing features is to avoid reinventing the wheel.
Ports-like tools work very, very well on Linux. Binary distribution works fine too. Also, the shared libraries of each application don't have to be (and usually shouldn't be!) bundled with the application.
Finally, I'm concerned about the MIT licensing, with all the GPL code floating around in that repository.
"As an application author, I want to provide packages for Linux desktop systems, without the need to get it 'into' a distribution and without having to build for gazillions of different distributions."
So you are a developer. You don't want to build gazillions of packages, but you want to target lots of users. Suppose you build a package for one distribution. Good luck convincing all your users to switch to that distribution.
I guess you are using Arch. Suppose the developer's opinion is that Gentoo's package manager is better, so he only bothers making a Gentoo package. He then tells you to switch to Arch if you want to use his app. Will you seriously do that?
I am sorry, but if YOU, the author, will ship MY GPLed library with YOUR application, then YOU are FORCED to open YOUR code under MY terms. Understand?
Don't steal my code, please. Don't bundle it with your proprietary app without my written permission.
I get the source, I follow the instructions for building and installing it (usually 3 commands; one to configure, one to compile, one to install). That's usually enough to get it working on just about any distro.
If I'm feeling especially up for it, instead of running the install step immediately, I throw together a PKGBUILD so I can use Arch's package manager to manage it (like this one: https://aur.archlinux.org/cgit/aur.git/tree/PKGBUILD?h=therm...). Gentoo has a really similar system, so I could just about copy the dev's script wholesale. Then instead of running the commands myself, I run "makepkg && sudo pacman -U *.pkg.tar.xz".
Oh, you mean for "regular users". Yeah, if you want to support those, you need to do some legwork. Regular users who have no intention of learning how to use Linux usually aren't (and shouldn't be!) using Linux. Mac OS and Windows have support teams and wide adoption. Why use Linux if you don't have to?
Please note that I'm not trying to sound elitist. But why would you use an operating system that has a steeper learning curve as a regular user?
I'm actually happy that Linux lacks a central concept of package manager because it encourages experimentation. Everyone gets to figure out what kind of package ecosystem they want to see most. We get to choose instead of just getting whatever comes with the computer.
Ports-like tools work very, very well on Linux. Binary distribution works fine too. Also, the shared libraries of each application don't have to be (and usually shouldn't be!) bundled with the application.
Finally, I'm concerned about the MIT licensing, with all the GPL code floating around in that repository.