the schism between looks/personality isn't completely arbitrary, but it is certainly context-dependent. having said that, to deny how important looks are is just wrong; looks get you through the door, while personality is what makes a person stay. personality is dependent on socially desirable traits, and rarely are men who are well integrated into society lacking in this. they go hand in hand. someone who is genetically attractive will certainly have more room to maneuver, but an unattractive person will need to appeal and manufacture traits which might get him laid.
it applies both ways, since both implicitly contribute to the damaging standards and expectations associated with both sexes.
status is something that is becoming less important in modern dating, i think. dating culture is oriented towards dating apps nowadays, and their prevailing attitudes bleed into everyday life, as seen, for instance, in the equal emphasis on clubs with more or less the same screening process. but if by status we mean certain normative expectations applied to people as, for instance, the expectation that an individual be well-integrated, then this ties in closer to personality generally serving as a fitness indicator more than anything