Me too. I have only had one job where I was specifically hired because of my broad range of skills and experience. It was with (at the time) a 6 person company. We grew and a couple of years later were merged with a much larger competitor.

Seems to me recruiters are only interested in people already doing exactly the job being advertised. As if somebody with lots of experience in lots of technologies suddenly can't come up to speed with a different product/tool.

This. I've learned it's best to masquerade as a committed specialist in order to get a job. OTOH, saying "I'm going to do whatever is needed to help your company succeed" isn't great marketing.

Same boat here. Do we need a hiring market specifically for generalists?