For women that chase rich men (not saying all women do this, but the existent and very small subset of women that do), it's often not because of the success implied. It's because of what the paper can buy.

Those women would still chase trust fund babies -- they chose to be born to those parents just as much as you chose to be cute.

Those women would still chase those that became rich out of pure luck (eg.: lottery).

Your financial success says nothing about your ability to succeed in interpersonal relationships. In fact, sometimes qualities between the two conflict with each other : being 'aggressive' in business is a sound plan to boost your competitive abilities, being 'aggressive' with your girlfriend just sounds abusive.

The whole reason the social consciousness regarding the idea of a "trophy wife" exists is to describe shallow women who emphatically don't "love you for who you are".

Also, there's a bit of philosophical conflict when it comes to the significance of "characteristics you can't do much about". The thing is, you often can't do much about any of your characteristics.

I think you're trying to argue that personal characteristics, like being smart, being funny, or being relatable, are somehow more of a choice than being pretty. But do you really have a "choice" in being smart or being funny? Isn't the grade schooler who opines after a girl who values these seemingly choose-able personal characteristics not trying his damn hardest to have those characteristics? If so, why does he fail when he does? Didn't he have a choice? No. He couldn't do anything about it, much like he couldn't do anything about his physical attractiveness. Yes, he can learn from his personal flaws and adapt his personal characteristics, but, first off : that relies on the meta-characteristic of being aware about your characteristics, which, again, not a choice or anything you can change about yourself.

Is having the characteristics to be rich or successful something you can "do much about"? Then why doesn't everyone do something about it to be rich or successful? If it's because they're lazy or aren't determined to work hard -- are those characteristics that they controlled? If it really came down to just working hard (which being rich/successful isn't, there's a lot of intuitive judgment that you either have in your instincts or don't, but that's a whole 'nother discussion), can you blame lazy people for being lazy? Did they sign up on being lazy? Do you think they chose to be lazy and undetermined? If not being lazy is so clearly better, did they ask to not be able to see that clarity?

We don't judge people based on how well they take advantage of their control, because ultimately no one has true control.

The series of actions required to become a multibillionaire with an amazing lifestyle and an absolutely lovable personality where everyone likes you is not some undefined series of actions that requires superhuman levels of magic. It's just that you don't know how or you are incapable of becoming said person; you don't know which human actions to take and decisions to make to become said person. So you become the best person your sense of control allows you to be, but did you really choose that control if it's given to you?

We judge people based on how well they suit our needs.

If one man's needs is someone who is funny and smart, so be it.

If another man's needs is someone who is physically pretty, so be it.