If your point is to stop using them until you have paid off the balance and request new cards, I agree.
But, you don't want to close all your credit accounts. That will hurt you later when you apply for new credit (mortgage, car loan, etc.)
Instead, I'd consolidate onto 1 or 2 of your cards -- the oldest accounts and/or no-fee accounts. Don't worry about interest rates... your goal is to pay them all off each month and never pay any interest.
Keeping the oldest accounts boosts the length of your credit history. Keeping the no-fee accounts are free, as long as you use the card about once a month to keep the account from being closed due to inactivity.
“That will hurt you later when you apply for new credit (mortgage, car loan, etc.)”
Not really. The only thing that hurts you is being late or not paying. A zero score is just as good as an 800 score. It means you have stayed out of debt. But your credit score will still reflect power bills and such so a 0 score is unlikely. People with 0 scores are usually housewives with rich husbands.