Headhunters are incentivized to chase you constantly, regardless of how many positions they are hiring for. The positions may soon exist, may have already been filled, getting advertised by multiple agencies - doesn't matter. These people are going to reach out, get you booked in and even if that specific position does not work out, they will be hopeful to get you into something else. Observe the same with Estate Agents - they will continue advertising already let/sold houses, just with motivation of getting you into their contact list hoping that it will be useful very soon.

The fewer jobs are available, the more desperate recruiters become to earn their commissions.

Then that wouldn’t be zero correlation.

Yes, that would be negative correlation.

When there are too many recruiters in the industry for the amount of positions that need to be filled, the remaining recruiters need to work their butts off. For some of them, this looks like emailing more people.