California has no way of charging them sales tax, nor should they, without a nexus. Imagine if you, living in CA, ordered something from a brick-and-mortar store in New York. If that store had to charge you sales tax and remit it to California, they'd simply say "no thanks" to your business. It's just not worth it for them to have to do all that work so you can get a $10 item (and so California can get their 82.5 cents).
Amazon shouldn't be treated any differently simply because they do a lot of business in the state. California knows this, so they come up with (well, Illinois came up with it) the idea that if some third party runs ads on their website for products on Amazon, that third party (an "affiliate") is actually an agent of Amazon. That's preposterous.
Amazon doesn't really have a choice, though. If they sue and lose, the entire affiliate program goes away. So they instead just drop the affiliates. They have to -- they're paying affiliates 6% of all qualified sales and paying the state 8.25%. And they are then open to audits and other nonsense from the state. It's just not worth the leads any more.