With the scenario that you laid out (ie. 5% and 10% loans), it makes no sense at all. The problem is, when you're in trouble the rates are never 5% or 10%.
Getting behind on credit cards sucks and is really hard to recover from. The problem with multiple accounts is that as the banks tack on fees and raise your interest rate to the default rate (usually 30%) when you give them any excuse (late payment, over the limit, etc). The banks will also cut your credit lines as you make payments, making it more likely that you will bump over the limit and be back in "default" status.
One payment, even at a slightly higher rate is preferable when you're deep in the hole because you can actually pay enough to hit principal. If you have assets like a house, you'll get a much better rate as well. In a scenario where you're paying 22-25% interest, your minimum payment will be $150-200 a month, and that is mostly interest and penalty. "One big loan" will usually result in a smaller payment, and you don't end up in a situation where the banks are jockeying for position so they get paid first.
The danger of consolidation is that you'll stop triggering defaults and keep making your payments, so your credit score will improve. Then the vultures will start circling and offering you more credit cards.
EDIT: Mea Culpa.
I wrote this based on experiences of close friends whom I've helped out over the years, not realizing how the law changed in 2009.
Back around 2004, a single late payment would trigger universal default on most cards, jacking all rates up to 30% and slashing credit lines, resulting in over the limit and other fees. Credit card banks generally apply payments (in order, to interest on penalties, penalties, interest on principal, principal) in a way that makes it very difficult to pay down principal for people deep in debt. They would also offer "payment plans" to entice you to pay Bank B vs. Bank A, which would trigger overlimit fees from Bank A.
Another change is that minimum payments were generally 2% of statement balance, which often didn't cover the monthly finance charge. The new law changed that, resulting in a payment of 1% of balance + accrued interest.
Under the old regime, consolidation made it less likely that various circumstances would trigger default, and gave the struggling debtor one throat to choke. With the new rules, there are definitely a smaller number of scenarios where consolidation actually makes sense.