I can customize a current project and then tick "Apply this (disabled tabs) to all projects in this portal".  This then mirrors the same tabs across all projects.

However when I add a new project all the tabs appear again. I would have assumed it would carry across to new projects as well, and it's very frustrating that it doesn't.

Can this be rectified?

I'm using a Project Template to create new projects from, so by default you should be able to apply to the tabs to the template at the very least.

Chris.