Half of the time, PPAs don't work. Snaps and Flatpaks are a step forward, but they still require a central server for fetching dependencies.
AppImages are good.
I don't believe this, and I suspect you're doing something unorthodox with your apt sources (it wouldn't be the first time I hear a story like this).
PPAs build from source on a vanilla platform for the given configuration, so they're guaranteed to have standard output (binaries etc.) and dependencies. When there is a problem with a certain configuration, such build won't be available to the user.
Can you list the PPAs that don't work?
Example: recently I had need of the of the DOSBox debugger, which you need to enable at compilation. On Windows this was as simple as finding some zip file from someone who'd done it and extracting the executable. On my Lubuntu system though, it wasn't in the repo for my version, nor was there a PPA. It was, however, in the very newest repo for Ubuntu and required up to date dependencies and I didn't want to upgrade my perfectly working base system.
Ultimately I had to manually download the package and its dependencies, extract their contents, and use LD_LIBRARY_PATH and the like to get it to run out of a self-contained directory.
That's what's fascinating to me. All the technology is there to distribute portable self-contained applications on Linux, but basically no one does it, or they pull a flatpak and still tie it into the horrifically silly repo model (and still aren't portable!). Only AppImage makes any sense, but hardly anyone embraces it.
At least the PPAs are actually a better solution than a platform like Windows (whose "system" is separated from "application"), where you download binaries for upgrades, since you have visibility of the source code and build process.
I have around two dozen PPAs for the software I need to keep up to date. In the past, I used to upgrade Ubuntu on every release; now, I barely do it on every LTS.