I'd court someone for the right position. Most of the recruiters are useless to candidates though. They don't really care about fit. In my experience, they often lie, or have no idea about important details.
'“Unfortunately the recommendation you made to drop one or two of our requirements,” the client wrote, “was frankly completely inappropriate.”'
It's the company's decision at the end of the day. But it's stupid to not listen to the talent you have contracted with to find you employees. They have knowledge of the market. Otherwise, what recruiter want to work for a place they know will have low fill rates due to uncompetitive offers?