if their mental capacity is such that they can't "help" but abuse the staff, are they really in a position to consent to sex?
This. I've worked in old people's homes and have been abused by residents. I have been punched, kicked, spat at, sworn at, as well as being felt up, had men (and one woman) walk right up to me while masturbating ... it kind of goes with the territory and, while a good home will do whatever they can to lessen the risk, it's always there because for some people with Alziemers this behaviour is a symptom of the disease. Often, it's behaviour such as this that is the reason relatives can no longer cope with caring for the person at home.
It's not just their capacity to consent to sex that needs to be considered. It's their capacity to understand that they are paying for it. Chances are, paying for sex is something this person would never have considered doing before they got ill.
And then, are we really saying that it's OK to expect a prostitute to have sex with someone who cannot control their behaviour? Who cannot help being abusive? Sounds a bit risky to me. What do you think, OLKN? you seem to have it all worked out.