iTunes already has my credit card info, and I don't feel like giving it another form of payment.
Then it's not really a matter of "my account is closed and I need to pay my bills", is it? Your opening post was a bit deceiving.
Different reward programs have different values. For mine, I can earn gift cards to various stores and restaurants or points for air travel and hotels. There's a whole list of things.
Ultimately, I can buy things with a debit card and earn no points, or I can buy the exact same things with a credit card (for the exact same cost) and earn points. Given those options, why not choose to earn points?
Oh, we got those type of thing here, as well; Air Miles, [Gas Station Name] Points, [Retail Store Name] Points etc. But it's proven that people are inclined to buy more junk when they get "reward points"; that's the reason most people I know stay as far away from points like those as possible, even if they believe they wouldn't be influenced. Just to be on the safe side.
It's not as if, for every 50 bucks you spend, you get a gift certificate for 10 bucks; most rewards aren't that high.