I never said that you "couldn't do anything useful in a destructor". Destructors are helpful in general for error handling in C++. I just said that std::bad_alloc is not a great way to handle the failure of small memory allocations.
It is true that printf would get you out of a jam in this case, because it doesn't throw the silly bad_alloc exception when it fails to allocate memory. You could also catch bad_alloc in your destructors whenever it pops up, and try to do something reasonable. In some cases, you can force the nothrow variant of new to be used (although not when std::vector and friends are involved.) But that is going to be very difficult in any non-trivial program.
I get annoyed when people talk about exceptions as a panacea for error handling problems. You don't have to think, just use exceptions, and your problems will magically melt away. The reality is, writing low-level code that correctly handles errors is very difficult in either C or C++. It's simple enough to avoid new and free, but once you start needing to implement transactional behavior-- either a function call succeeds or it fails, but it doesn't leave a mess-- things get difficult.
If you find yourself in a scenario where you have to undo changes that you made earlier to some data structure, your error handling may itself encounter an error. And how do you automatically handle that? Well, you have to engage your brain and structure the operation into a prepare operation followed by a commit operation. And that is not going to be trivial in either C or C++.