Not to get all Dave Ramsey on you, but this isn't a math problem, it's a behavior problem.
The biggest reason not to do this is because people are horrible at breaking habits--smoking, drinking, relying on credit cards. Now, if you are a few years into credit card sobriety and have an emergency fund to handle future unforseen expenses, then it would be okay to do this. If you woke up 2 weeks ago and just swore off credit cards then, well you probably shouldn't do this.