We at Thumbtack use a similarly simple form, and our chargeback rates are very small [although admittedly we aren't a particularly attractive candidate for fraud]. We also did see both conversion increases and frustration decreases when we switched to a simpler payment form.

We do have one difference though (which I would call a simplication): For the expiration date, we just have input boxes for the person to enter it instead of a dropdown. Select boxes are great if a) You can pick a sane default and b) you don't have many options. For a CC form, both of these fail. You cannot set the default with anything better than random accuracy, and each box probably has at least 10 options. Additionally, the expiration date box says "2 - February". I have a lot of credit cards, and none of them say the name of the month on it, only the number. Why waste the space?

The user just typed in their 16-digit credit card number, just pop them right into the expiration date input boxes for them to type in their month and year free-form. Don't make them put the credit card down, pick up the mouse, then have to navigate select boxes with tiny print.