Chase reps frequently ask that question. Good research is your friend here. Before you call for reconsideration or, if already approved, for activation, look over the card's benefits. There'll generally be one benefit, in addition to the miles, that you'd actually like. Tell them that's why you were interested in the card.
I applied for the Chase BA and then 30 days later, for the Chase CO. I noticed that the CO card actually has a very good rental car insurance policy that's included when you pay for your rental with their card. Unlike my Amex Plat insurance benefit for which there is a fee, CO's coverage is free. When I activated the CO card, I mentioned that benefit.
This is little stuff, I know. But I know enough about these customer call centers to know that the reps are generally being asked to take notes during their telephone calls. Those notes may (depending on how sophisticated a company's IT system is) be available for review by other departments, including credit card approval and reconsideration. If your standard answer is "uh, the miles" and you do the FT standard: meet the spending requirement, put the credit card in the drawer, and cancel before the annual fee comes due, I guarantee you some of these companies are likely to reject your applications more frequently.