They might... if those channels want to raise their rates higher than Dish thinks its customers would continue to pay!
Do you want your channels to double in price every time negotiations are renewed?
You mention negotiations, but it looks to me that even though there is about seven weeks left in the contract, there are no negotiations going on. All AMC Networks have already been removed from the Channel Line-up Card PDF's. How is that helping their customers? And the timing of the announcement, right after Dish losing a court ruling, makes it look like a personal vendetta by Dish towards AMC Networks. Once again, that isn't helping Dish's customers either.
Dish mentions that AMC isn't worth it's perceived value due to it's programing being available through alternate sources. But what is Dish's value if they aren't carrying a top 20 cable network (AMC), don't have a top network (Disney channels) in HD or have 24/7 HD RSN's (or in NYC any RSN's at all)? That's like the pot calling the kettle black.