It seems to me like joining the military is arguably more deserving of the phrase "selling your body"; you're basically signing up to get injured or killed.

I think the "body" in that expression is quite specifically referring to genitals, or the selling of your intimacy.

Because that's what's different from any other physical labour, the part of your body involved. That's the specific problem of sex work no?

It is a high risk job along the lines of coal mining and such, since it will result in an increase in transmitted disease risk. It's important to acknowledge that, but I am on the side of it being work. I just think we need strong protections in place and regulations to handle it akin to other dangerous jobs. Like, a sex work branch of OSHA.

It’s not even an argument really, it’s the undeniable logical conclusion that trading your labor and/or time for compensation is work, period.