No, not completely...
but...a key differentiator in Edlund and Korn's model is reproductive sex. Wives can offer it, whores can not.
Strangely..."This begs the question of why married men go to prostitutes (rather than buying from their wives, who presumably will be low-cost providers, considering that they can sell nonreproductive sex without compromising their marriage)." Guys, nothing says "Happy Valentine's Day" more than "low-cost provider."
Finally...the emphasis on the utility of children is puzzling. In most Western democracies, fertility rates have plummeted as wealth has increased. Empirically, men not only buy fewer whores as they get richer, but they have fewer children.
yes, supermodels do prefer aging billionaires. And Gary Becker proved it mathematically decades before The Donald married Melania.