packages don’t update with operating system updates using native package managers like apt or yum so updates are clumsy and in some cases have broken my system.

Sorry? AppImages shouldn’t be able to break your system, at all. For example it does not affect the installed system packages, except a tiny bit when you install AppImageLauncher because that comes as a system package.

packages don’t integrate with operating system menu hierarchy.

Check out AppImageLauncher.

It is for these reasons I urge the developer community to avoid using snap, AppImage, or Flatpak and stick to releasing binaries for specific distributions like .deb or .rpm.

I think you are in the exact opposite here. These solutions are exactly for protecting the system from package dependency inconsistency. Installing such an app won’t install any more system packages, and especially won’t possibly lock system package versions to some old version. They don’t affect the system package manager’s state. The entire reason for these being manageable without sudo permission, as a regular unprivileged user is that they don’t modify the system, but only the installation in your home directory.
As much as I don’t approve of snap, and dislike the resource consumption of flatpak, what you are saying is simply not true.