Yourself, those consolidation places are businesses. All businesses exist to make money. They tell you to stop paying the cards and instead pay them, they hold your money. The idea is that by withholding payment from the banks your cards are issued from, the consolidator can make the banks desperate. But, here is the issue - BY NOT PAYING BANKS YOU HAVE TRASHED YOUR CREDIT.
Further, the debt consolidator will pocket a portion of your payments and gain interest off of it. WHY PAY A MIDDLE MAN.
1 - Your credit gets trashed. So, even if you have paid off the debts - it will be on your history for 7 years that you were unable to make payments on time. The consolidation companies conveniently forgot to mention this in their commercials.
2 - you still end up paying back all of the debt, usually over a longer period of time.
3 - the company gets free interest accruals while holding your cash.