Try testing several themes on your site without disrupting how it appears to your visitors. You will appreciate the Customizer more.
Try implementing several CSS or theme option changes for your client’s site and get the client approval before the change by sending a single link for them to preview the change. You will appreciate the Customizer more.
I think the Customizer used to be very slow, but it was improved a lot right before Weston left to work for Google.
It is a lot better than having different settings pages for each theme.