On a VPS, it really doesn't matter if the hosting company has your root password or not - they can directly access the filesystem to view or modify any files any time they want.
For some virtualization types (like Xen and KVM) it is more convenient for the host to know the root password so they can login to manage the VPS. Without it, filesystem access requires that the VPS be shut down, with is worse for everyone.
For other types like OpenVZ, the host can login as root any time they want, without even knowing the password.
In the case of GoDaddy, they would probably be better off setting up VPSs they sell with an additional root-equivalent account or using SSH keys - that way the customer can keep their root password secret.