You're getting dragged in the discussion below, and while I think I understand your more specific points below, I'd like to offer some perspective on this general point instead of continuing down those lines.

Here you've set the tone by calling sex inherently shameful. Not being serious/dignified isn't the same as shameful. For me, shame comes with some moral failing. I'm ashamed when I disappoint someone, or get angry for something petty, or act petty myself. Not because of being undignified. I'm not ashamed when I fart, that's just my body. However, I am ashamed when I fart in a public place, because it's smelly and few people deserve to suffer like that.

So my counterargument to your perspective here: sex isn't inherently shameful, but it can be because of context. Banging too loud when having guests over is shameful: not because of being loud, but because of the lack of consent - being too loud when everyone around consents to that kind of behavior is fine. No shame if you're in a place where everyone is hooking up, and everyone knows the walls are thin. That's just fun. Not dignified, not serious, but fun. So the sex part isn't the problem. Not inherently.

To the main point - if everyone would just be cool about sex work, I honestly think folks wouldn't ascribe shame to participating in sex work. I've lived in small communities in the Amazon where there was essentially no shame associated with consensual non monogamy, outside of the religious folk. Different social structure and beliefs in that region made it much more open...so I heartily reject calling sex a shameful act. That's too much moral baggage to ascribe to such a natural, zesty enterprise.