I have never seen Ubuntu Software Center ask for a root password. It's not supposed to, and it won't happen unless you do something special to your system. What is supposed to happen, is that it uses Policy Kit, which will ask you to select a user and enter a password for that user.
PolicyKit is much more suitable for this than gksudo, since sudo will allow access to commands, whereas PolicyKit allows access to actions such as org.debian.apt.install-or-remove-packages. If instead you provided access to run apt-get, then you could do anything apt-get can do, which is way too much power. You might, for instance, grant permission for all users to install security upgrades from official Ubuntu archives, but not allow the user to install new software. That wouldn't be possible to do with sudo.
I would check to see if you've removed the package policykit-1-gnome.