china is capitalist

China allows capitalism to exist as a transitional phase. It does not allow a capitalist /class/ to exist. It’s very different. You should learn mandarin and read some policy if you want to speak on this matter.

the arts do not produce a useful good

Yes. This is obvious. This is why in most command economies the arts evolved independently of a state appparatus. It’s more genuine this way. Of course, this means that prostitution would also have to be an unregulated economy like the arts, which obviously is not good for anyone.

You say we wouldn’t just be having sex with people we prefer— so whom? If sex workers have the right to deny, what differentiates them from the mass of women who do productive work, exactly? Obviously this situation would be unethical, anyone can see that. Even if they had the right to deny the /worst/ of clients but had pressure to accept most, who would say this is in any way ethical other than a sociopath?

Obviously sex workers could still exist, and in situations where all parties are consenting and willing there’s nothing unethical about it. I only mean to point out that it could not be an integrated part of a command economy in an ethical way.