The existence of Flatpak etc. is a misguided concession from the FOSS community to private businesses and to software developers who are used to packaging for the cloud. The model is not appropriate for desktop or mobile software -- there is a reason that filesystem access is extremely restricted or impossible on mobile platforms, and that even Android has moved to dynamically prompting for permissions when apps use them rather than bundling them into a single prompt at installation.
For Flatpak to work, we need MUCH heavier sandboxing, which will be detriment to productivity for desktop users for certain classes of applications, and may prevent many types of applications from being packageable as Flatpak. I think this is a fine compromise. I'm OK with installing Spotify as a Flatpak (given better security, not now) but keeping my webserver, database, file manager, terminal, programming language, and other "system" software in the OS repository.
They just use some combination of rpath fields and virtual filesystems to make sure the dynamic linker only inspects the paths mandated by the application author.
And that's what we're talking about, effectively; how self-contained and sandboxed the package itself is.
Sidenote: I include docker as a package manager in that list because recently I actually ran into a very large and popular command line application that, per their documentation, prefers distribution and execution via docker over anything else: aws-cli. They don't keep any other linux package managers up to date, despite having a package in snap and distributing a .tar.gz. They recommend invoking it via docker. Rather interesting, and I'm surprised we haven't seen a frontend for "docker as a pm" gain traction, to increase usability over "go into your .bashrc and alias aws=docker run aws/aws-cli:latest $*"