You knew the warranty terms before buying the machine, no? You essentially took a risk and you lost.
I feel bad for you, but you know that once that 1 year warranty is up, and your machine bums out after 12 months, they're not going to fix it for free anymore. I don't think what Apple did was unreasonable even if you'd think that their display SHOULD be problem free for longer than 14 months. It's not like they control these things. Some people have displays that have lasted for over 5 years with no issues. It's random bad luck.
Get the extended warranty next time to feel more secure, or get a Dell 24" even if it's less colour accurate. Calibrate often. Leave it turned on for 20-30 minutes before using it for anything requiring colour accuracy, and you're set, since you have their 3 year warranty.
I think the problem is Apple skim out on their Warranty on their high price Apple Hardware. You only get 1 years, and 90 days to call Apple Care then they will stop talking to you. It's like they want to make a lot of Apple user buy Apple Care. They should make Apple Care cheaper. Spending $2,000 on it is expensive already so people will have a hard time putting in the extra for the Apple Care. They need to lower their Apple Care service if they want more people buying it. But, it's alway a good ideas to buy extended Warranty just to be safe when you are spending this much. Even if you have to pay so much like Apple notorious for everything being expensive.