I’m going to agree in part and disagree in part with your assertations, especially based on the line above.
First, the agreement. If (the niggle!) the relationships are fully consensual (pretty much a given) it isn’t any of our business, assuming all parties are of sound mind and legal age. I think the problem is that they do not enter into the relationship with any degree of equality in most of the “rich old man, young attractive women” tropes. The man is paying what the market will bear for a bit of eye candy, and presumably sex.
The female in this (yeah, there’s the possibility of it being gender reversed but it’s extremely rare IRL) is not normally going to be able to afford the high priced lawyers, the detailed reviews, and isn’t arguing from a position of strength in the first place unless they’re wealthy/famous/etc in their own right.
So there’s a major power inequality in the relationship and bargaining positions. Now, again, back to the agree, most of us who would argue that legally protected and regulated prostitution should be legal (a not insubstantial number) should equally support a more formal version of the situation, which this scenario is in the most cynical sense. But the same concerns exist for prostitutes being in positions of unequal power and protection under the law, as the police and courts tend to favor those with power and influence.
Lots of maybes, situational issues, and the rare misunderstood love matches, but again, I feel that beyond the romanticists among us feeling it’s “wrong” on some level, most are concerned that it’s nigh impossible for there to be a truly “fair” consensual and contractual relationship. Note - fair can and probably should work the other direction as well, where if some 70ish multi-billionaire falls for a 20 something and marries her in a fit of passion without a pre-nup, expecting them to receive 50% of their estate after three years if there was no contribution to said estate. Nor should his heirs be able to say she deserves nothing either.
But, going full weasel, in my heart of heart, I do mostly agree that if all parties are sound of mind and body, and the compensation is reasonable and protected, that I don’t find that I have any right to “tut-tut” even the most mercenary of relationships.