Getting a bigger credit limit only to use it for larger payments just means you cost them more.
I can't figure out why you'd cost them more. Please clarify.
It's mostly an opportunity cost kind of thing. With every credit card I've ever had you pay no interest as long as you pay off the balance in full by the payment date. This means that, if you always pay off the balance, the bank is effectively giving you an interest free loan from the time you make the purchase until the time you make the payment. The bank could invest that money they loaned you in just about any other investment and make more than 0% return on it. Giving you a bigger credit limit just means they'd be allowing you to take an even bigger interest free loan.
That's the way the credit card companies make money off of _you_.
They also make money from a percentage (or sometimes fixed) cost of everything you buy. So if you use a credit card daily and pay off $800-1000 every month, the credit card company makes money on that account. They need to make at least enough money each month one way or the other to justify managing the costs of dealing with your account.