As I've just said, the only time you should do this is if you're *certain* you are already paid more than most if not all companies would offer at their top end. Then at least you would filter them out. And yes, the part about making financial sense is then relevant.
If you're paid in the middle or heaven forbid the bottom, all you are doing his anchoring low. What incentive do they have to pay you top dollar? Likely they will think giving you a few K extra is enough.
I don't think they're supposed to ask your current salary. She made an offer, I said it wasn't that much higher than my salary at the time, she said she'd see what she could do, and came back with a higher offer.
You say what you think you're worth and literally nobody can tell you that without knowing a lot about you and there isn't a magic spell that you can cast on the recruiter that will maximize what you get. For that you need skills which most of you don't have: negotiation, business and people.