You still need to distribute the static executables and there's no way to update them besides downloading them again unless the software has some auto-updater built-in. That definitely doesn't solve the issue.
I'm not sure I follow your reasoning here. If you are so concerned about the security of your system that you want to run each program on a sandbox, then you definitely do not want to allow programs to "update" themselves by automatically downloading random binaries from the internet.
Well, I never said I was concerned with security. I am to some extent but not to the point where I inspect every single update.
What I value most is having every software or library available through some form of package manager. Downloading static binaries off the internet without auto-update just doesn't make it which is why I like having Flatpak as a fallback.
It also makes it easier for the common user to have every piece of software available through one store. They don't need to know whether it's a .deb or a Flatpak underneath, it just needs to be there and work reasonably well.
There's really no other option: either distro maintainers include every single piece of software in the repositories (unlikely), or we need a common format that works on all distros (already the case with Flatpak).
This "issue" was already solved by static executables. Snap and flatpack are the work of computer illiterates.