I've read through these comments and I have yet to find a legitimate reason for all the "Customizer hate". So far the only criticism I have for the Customizer is what Neo mentioned, there needing to be an import/export settings function by default. But as he also mentioned that it's fairly easy to create your own hook to save customizer states which is what I've done on various projects. Then there's the "is_customize_preview()" function that can be leveraged on the preview screen itself.

I would love for someone to write an in depth itemized article as to why the Customizer is the Devil, because so far I have nothing but kudos for the api. I understand it's not perfect, and it will continue to grow but it's far superior to most of these settings pages I've encountered in themes that look like one of those daunting computer control panels you'd see in a bad 1970s sci-fi flic.

As far as clients are concerned, generally the first thing out of their mouths when they use the customizer for the first time is "oh cool, I can see changes in real time..."