The key issue is if there might be members who WOULD respect her should she become a member. Given how Chuck has reacted to her thus far, I think the answer to that question is at least potentially yes. Would that be enough for her?
Why would she need anyone to respect her if she has something substantial for them? A club member respecting her shouldn't matter in what she can gain through giving what she has, clearly respect wouldn't increase the value of her offering at least not for someone with an IQ (unless the value of what she can offer is not as good as you are suggesting and patrons go headfirst into something risky, risking their position like she did, out of respect for her, which would be laughably unrealistic). For that reason she could have gained from what she can offer the same results without joining the club. Joining the club for something she already has should be out of the question, considering this is 21st century if you have something to offer you will be entertained whatever you are, trophy wife is no exception.
Also, the chief of police is Jim, not Eric.
Doesn't matter I knew I could be forgetting the name, that's why I added police chief.
As for why she does not simply meet outside the club with the club members, @ffive already gave some explanations.
You mean he give some absurd explanation that she couldn't even get someone to listen to her?, but he couldn't convince me, she could have done that without risking her position and without losing much dignity as compared to joining the club. It's just this VN where someone like her would have to join a stupid club to gain from what she already has to offer.
Something else just came to mind:
So by default her joining the club should raise some eyebrows as to why she did it, clearly people would be more skeptical of her motives, they would know/believe that she is desperate for lacking something in life or just fed up of her situation in life (Elias situation) that should realistically decrease her negotiating position in a real world scenario vs if she approached the same patron with the same offering with a high head and zero sign of desperation.