I'm sure that's a major part of it, but I also wouldn't want to live in a world where we could only get aspirin from willow bark. We either wouldn't have enough aspirin or we wouldn't have any more willow trees. Medicines derived from the actual source aren't possible on a global scale in most cases.
Capitalism is a blight on society and has lead to countless deaths. But in a utopia where money doesn't exist and people create medicine for the world only to help people with no profit they still need to synthesize it.
But if it's illegal there wouldn't be legal brothels around?
And I haven't followed through but I've looked into prostitution in my area through various means. There do seem to be fairly moral options in my opinion. People who work independent and interact directly with the customer and they keep all the money. They have their own space to meet and they have the option of refusal at any time.
I'm not saying you're doing this intentionally, or that what you're saying is harmful, but I do worry. It feels like you're demonizing an entire industry and adding to the idea that it's immoral unless done through brothels. Sex work is work, and while often people end up there out of necessity, that's not much different than any other job people work these days. I would say that people who knowingly pay for sex work where the worker doesn't have their full autonomy is, at best, selfish and shortsighted.
Or are you saying that because it's a crime, by paying for it they're contributing to the sex worker also doing something illegal and that's bad?