Criminalising protitutes’ clients harms prostitutes

The government is considering making it illegal for a man to buy sex from a woman. Chris Dillow has an economic analysis of why this will harm prostitutes:

Just how stupid or evil are New Labour’s women ministers? That’s the question raised by their support for making the purchase of sex illegal.
Basic economics tells us that such a move would be bad for women who sell sex. A simple supply-demand diagram should make this clear. If the purchase of sex were legal, the demand curve would be D*, and the price of sex P*. Now, if the purchase becomes illegal, some men who bought sex at P* would think “yikes! I could get done for this. I’d better stop.” Demand would then fall to D’ and the price of sex would fall to P’.

Prostitutes would then be worse off. It’s the women who would suffer. [...]
What’s worse, the main losers here will be the most vulnerable prostitutes – the ones on street corners rather than Chelsea horizontales. [...]

So, criminalizing buying sex would hurt prostitutes, especially the poorest ones.
Which raises the question. Why do New Labour women not see this? Are they stupid or misogynistic? Or is this yet another example of politics as signaling?

I’m sure it’s the latter. I doubt if the ministers gave any thought to doing an economic analysis on the matter — I certainly didn’t; then again my background isn’t in economics so it’s perhaps something I wouldn’t naturally think of.