You're assuming printing money causes inflation (or the removal causes deflation) and nothing else. But this isn't true.
Adding money to the system IS valuable, in that it helps maintain appearances. In a social engineering system, that's very important. (Whether it's right or wrong, against some moral framework, is up to you. The system is just a system.) Point being, in a recession, the economy shrinks, causing deflation. Deflation causes positive feedback, and you get a depression. By adjusting interest or (when that runs out, as it has,) printing money, they can hold inflation constant, so the economy looks stable and people can keep on with their lives, rather than not being able to buy anything because Wall Street is in shambles*.
*Remember, when the rich are doing well, everyone has it normal. When the rich are doing badly, everyone has it bad (whether out of spite, or actual economic dependency). This is probably what was meant by "trickle-down economics", not an actual cash flow.Tim