Moving core menu items to the customizer would be a good idea IF the results in the customizer were better than what we have now. I think most people would agree that the customizer experience with widgets is a huge step backwards from the existing functionality. For me, it's so significant that I make extra clicks to AVOID getting the customizer version of widgets because everything I do there will take longer and won't be as well done as in the existing widget area.

This really appears to be a case of a lead designer who is incredibly attached to a product, and it looking for a way to use it, even if it's a truly bad application. The customizer isn't even a really great way to customize themes, it's only saving grace is being somewhat standard. Yet most themes tend to have their own setup and options areas, as the customizer perhaps is a little too restrictive or time consuming to program to.

This is really an area I wish Wordpress as a whole would just stop and take a step back, and really think about it before they burden everyone with a poor UI and UX, one that makes this more complex, less standard (because themes can too easily change it), and more likely to create confusion especially with more basic users. It's also likely to frustrate experienced users by making everything they do slower.

I honestly wonder if someone at Wordpress is just trying to make this as complex and diffcult to master as Drupal or Joomla.