I know that Miele has at least one, but don't think it is available state side.

8-10 years ago there were quite a number of white ones. It wasn't a popular offering and seemed to disappear overnight, possibly in reaction to the economic meltdown. As soon as you have more than one color, you way increase your inventory costs. Black goes with a lot of kitchen decor, and many of the "stainless steel" appliances people have to have on a knee jerk basis are really black with steel appliques, so black is a choice that matches in with the other appliances.

I imported my induction cooktop to have something that wasn't available here. To do so, you have to make sure that your building code doesn't specify that appliances have UL listings (look for the words "or equivalent" if UL is mentioned), and get a letter (on paper) from your insurance company that a European certification is okay for them (mine just required the installation be done by a licensed electrician). Then you have to find someone in Europe who will sell it to you. It can be shipped by FedEx, who will take care of the duty and bill you for it, or you can have it sent by boat.

You won't have a warranty, but if you have a local independent Miele service agency, they should be able to fix it if necessary. AEG used to always have white, and may still, but it would be harder to get service for them if you're in the U.S. I was also warned about the Hertz. My local Gaggenau service guy said it wouldn't be a problem, but it might affect the clock. In reality, there are other places, besides the Americas, where 60 Hz is used, and mine was made to work on either frequency. I wouldn't be surprised if the Miele were as well.

Not sure if you have seen the silver/mirrored finish - Thermador makes one and so does GE. Not white but close!

The white paint fades to brown over time.

White paint? Or did you just mean color? It's certainly very possible, especially if there are plastics or resins involved. White paint (usually a metal) doesn't actually brown. White quartz counters brown because the resin that holds them together browns. The white cooktop on my portable that sat in the window didn't fade appreciable, though the white plastic housing did.