While that certainly seems like a logical move and a good thing to do, it simply might not be.
Opting out has a major advantage of leaving your interest rate alone but the major disadvantage of having that card reported to the credit bureaus as closed. Once that card is closed it no longer gives your credit score a boost by having a long credit history. And that’s an important factor in having a good credit score.
Average Age of Open Credit Lines Credit history is a significant component of your credit score. As such, the average age of your credit lines can be a strong indication of your credit history. Care should be used in keeping old accounts open, active, and in good standing. Source
A better option might be to actually address the underlying problem, the debt. If your problem is that you are unable to pay off a big balance on your credit cards then maybe you should investigate LendingClub.com, the peer-to-peer lending network, where you can get a loan at a lot lower interest rate than from a bank.
Using that loan you could pay off your credit card balances and NOT close the card. The goal would be to keep open your three oldest credit cards open and get the benefit from the long history on those cards. If you are unsure which are your oldest credit cards, get a copy of your consolidated credit report and check the reported history of your cards.