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I was sent this same e-mail today for my Chase Amazon Visa. Upon clicking the link it tells you that you're only eligible for a certain amount like the OP stated. Mine was only a measly $500 more. I took it though since it requires no HP.
To answer your question about why they did not just auto cli your account. They may just want an updated income, especially if your spending pattern has been flagged.
I took their CLI to 14k, if only to lose the .5k from my 12.5k ;-) There's no option there to enter what you would like as your new CL and no counter-offering. It says if you want a higher one, feel free to call the number on your card and it will be a HP. The new CLI was reflected immediately in the account management website.
Now it's just Discover at languishes at the initial 10k starting limit they gave me two years ago....
Consider your self lucky to have a Discover with that kind of limit. Most people have trouble even getting 5K.