Here are a few possible reasons:
As already mentioned in mhoran_psprep's answer, the card provider can save money if people don't sign up, while continuing to advertise that they give a 5% rebate (or whatever benefit).
They may use this to get you to do things that help them. For example, they may ask you to switch to electronic billing if you still receive paper bills through the mail.
They may try to get you to use their other products and services, and sometimes those of their "partners" (companies they team with to provide some of these discounts, rebates, etc.).