>So the only way to make something "run for a long time" as a power source is to really really slowy take energy away from it. Why would we bother to do that?

I agree with everything you're saying, but there are some fairly obvious answers to this question, because there are plenty of things that require very little power but that are difficult or impossible to service and thus you want to last a very long time - pacemakers, for example, or certain robots designed for space that use very low power, very long lasting nuclear power sources.