X10DT installs only part of CDT; Cannot create a plain C project

(Cal noticed this.)

If you try to do New > C project
you get a NPE. Before it gives you a choice of new project wizards.
(You can see the stack dump in the Error Log View)
java.lang.NullPointerException
at org.eclipse.cdt.ui.wizards.CDTMainWizardPage.switchTo(CDTMainWizardPage.java:425)
at org.eclipse.cdt.ui.wizards.CDTMainWizardPage.createControl(CDTMainWizardPage.java:93)
at org.eclipse.jface.wizard.Wizard.createPageControls(Wizard.java:170)

Not all of CDT is getting installed, just the parts that Emmanuel's code requires for his stuff, I suppose.

I installed all of the CDT "Main Features" from the CDT 6.0.2 archive (and annoyingly it's still going to eclipse.org for cdt.doc.user and maybe some other plugin parts. grrrr)
Now I can make a new C project just fine.

So, the parts of CDT that X10DT pre-reqs does not install a complete set of CDT.
Not sure if we want to do this or not, but I'm documenting it here.