It's likely because of the way the Amazon FPS API works. You can set it up to pay directly to a third party while keeping a cut for yourself. That way Kickstarter doesn't have to act as an intermediary that collects the money and pays the project starter.
When Kickstarter started, the types of payment logic they needed (user approves payment now but don't execute it until later; user feels like they're approving one payment, but it is split between multiple recipients (Kickstarter and the project owner)) weren't supported by PayPal, but were supported by Amazon Flexible Payments Service
In 2009, PayPal rolled out a set of very similar API's that would allow them to do these things (see http://x.com). I would guess that the fact that they haven't made the switch is just a matter of inertia, the difficulty the transition might present, and having more important things to work on, but I'm not intimately familiar enough to know if there are other reasons they might be staying.
I do know that a friend of mine had a startup that started on FPS but was very, very eager to switch to PayPal when X came along because FPS presented so many problems. They were a lot smaller and less wedded to the platform, though.
It's reportedly due to the nature of how Kickstarter handles transactions: they don't process payment until after the funding period closes (and only if the project meets or exceeds its goal). Amazon Payments is basically the only payment processor that allows this sort of "delayed" charging from what I understand.
because Amazon payments allows you to agree to pay at a later date and cancel that for whatever reason, Paypal etc. do not support this (as far as I know). I also assume the reason you can't use the site (as a project creator, anyone can use Kickstarter as a backer) is because of tax issues.