That a plan might be possible that would allow him to achieve all his goals will not benefit him if he doesn't think of it, and there is no guarantee that he is capable of thinking of it. Harry is a very bright boy, and the laws of magic allow a lot of cheating. But there are a bunch of reasonably intelligent opponents out there that would be opposing his efforts, and the Harry of this story is demonstrably not smart enough to calculate in advance all of their possible countermoves and preempt them.