I can't see any reason (aside from avoiding processing fees) not to provide an Amazon payments option for UK projects
I can see a big reason (apart from Amazon UK perhaps not supporting this the way the US one does, which I'm not sure about). They probably want to open Kickstarter to more countries in the future. They can't count on Amazon providing the service for every country, so they would eventually have to create their own system. Might as well do it now, instead of having another intermediate step.
Also using Amazon is a liability. If the Amazon service fails (which happened a few days ago), Kickstarter can do nothing about it. If pledges don't go through because of Amazon's system, again, Kickstarter is helpless. I'm sure that Kickstarter would rather have its own system over which it has more control. (And of course it could cut itself a larger cut, and optionally give project creators a larger cut.)