As you have found, when Project Server provisions a new Project Site for a project, the Project Owner is automatically granted permission to modify anything in that project site EXCEPT security-related settings.
Although there is a site template that the system uses to provision new Project Sites (you will find it when you manually create a new SharePoint site in the system), there is no way to configure the system to grant the Project Owner FULL admin-like rights in the Project Site without investing in a custom-developed solution.
In the meantime, a Project Server Administrator will need to manually change the Project Owner’s rights in a new Project Site after it is provisioned.
