One Example? I have been disabling what Apps get access to on my Blackberry for I don't know how long. Forbid Whatsapp to have Access to the Camera? No Problem, if I want to make a photo from within Whatsapp it then says something that it isn't capable of doing so, just how it should be.
How a Browser behaves in private Browsing also is a browser-side issue. Whether or not the API allows Extension developers to give users the functionality NoScript for example provides to its users it also a browser-side issue.
See for example here (you won't see Google spearheading this cause) http://techcrunch.com/2015/08/14/mozilla-makes-private-brows...
The distinction between "This concerns only the Extensions" and "this concerns only the browser itself" is not as clear and easy as you say it is, especially in this case.
Since Google is all about obtaining information and using it, I don't think they are to be trusted in developing a browser that is highly concerned with user's privacy. Everybody has to make their own decision.