I'll repeat my comment from the Make post here:

While I think this functionality is useful, I think the Customizer is the wrong place for it. That also extends to post/page editing btw. Using the Customizer for content creation blurs the scope of the feature by mixing two very different types of tasks into one tool: Customizing the appearance and functionality of a site vs. creating content for the site.

I can see this type of feature creating a lot of confusion for the end-user, especially those who are not already well versed in how WordPress works.

IMO for this concept to work, there has to be a clear separation between the Customizer action (creating and customizing a menu) and the content creation action (creating and populating Pages). This separation needs to be both contextual and visual, either by moving focus off the Customizer to a new and different Editor panel, or by enabling in-page/post editing directly in the preview.