My big problem with it is uninstallation. If I ever want to remove the program, I have to 1. Hope that the author published an uninstall.sh, or 2. examine the install.sh to see where it spams all its files to and remove them manually. This seems like a major step backwards from package managers.
This is the only reasonable argument I've heard, but in reality I don't find uninstallers do their job anyway, i seldom have an uninstaller that doesn't leave empty folders behind, config files, user files...
