I think the most reasonable explanation is that unobserved things do not happen, at all, or only happen on some abstract statistical level.

That doesn't imply that consciousness is special. The reason why you are aware of reading this, if you are indeed aware of reading this, is that your life matters for some future event, which on the fundamental physical level has already happened, but its exact results depends on how your life unfolds in some way. If I locked you up in an impenetrable box that is to be completely obliterated at some future point in time, so that whatever you do in the box would make no observable difference, the rest of your life in the box would not happen.