I had a closing recently where they wanted a certified check. I told them I was sending a regular check and I didn't care if they waited an extra week. No issues.
Not taking a credit card is understandable. It's not just the fee. The ones that take them tack on the fee. It has more to do with a buyer having remorse or thinking the closing is taking too long and trying to back out of the deal by filing a dispute.
Like Dioxide described, I haven't seen a by the book closing company take a credit card. By the book as in one that sends a settlement statement after everything is finished. Not many associated with a mass seller actually does this but TCS in Orlando comes to mind.