>Or could it be because the traits one needs to cultivate in order to achieve high status have an overlap with the traits that are desirable in romantic partners (e.g. empathy, integrity, being an active listener, knowing when and how to compromise)?

You do not need those traits to be high status.

>If that is true, why is it true? I think that's a far more interesting question.

Almost any scientific finding should be ended 'but more research is needed to be certain'. Perhaps the question to ask is why isn't this getting more research, given just how important the topic is to the lives of so many people. All of the questions you raise can be tested with further research, so why aren't they? Why is some of the best data (best is not to be confused with good, as best is relative) from dating web sites?