freezet I think you misunderstand the password prompt that you get on desktop operating systems. It's not to "allow install app x", it's "allow app x to be written into these system folders". This is based on the ACL of said folders which are often restricted to rwx for root/owner and have more restrictive permissions for group and others.
Since installing apps on mobile operating systems under no circumstances touches the system folders, there's a lack of password protection. I don't really see any benefit of this, since you already need to confirm the installation of an app if it is installed for the first time and as another user already pointed out, it's redundant for updates because of matching signatures.