> There's just one problem: they don't integrate with desktop without an additional application

Their biggest problem is that they're not actually truly portable between distributions. They're a gamble of what they're compiled and bundled against, and it's possible for two distributions to not have binary compatibility with each other due to user space differences (different versions, compile flags etc). The kernel developers may not break userspace between updates, but userspace developers certainly have no qualms about breaking userspace.

When you head out of Ubuntu/Debian where developers often build AppImages on (because Linux is a neglected platform and when they think Linux they think Ubuntu), they often fail to run or have errors (e.g. on Fedora). There's more problems such as the terrible practice of encouraging people to set the execute flag on binaries they download off the web.

Flatpak avoids the dependency problem entirely because it's uses runtimes and namespace to ensure reproducible and stable runtime environments.