I mean HR has to be desperate, not the job seeker.

HR people would hire them, were it not for the experience of these people leaving the moment there's a better job.

Overqualified is a proxy for how likely are they to stay in the position long enough to make it worth hiring them.

For high turnover roles, like entry level retail or restaurants, there is no problem hiring someone overqualified; when they leave in 3-6 months, that's par for the course, the business is always having to hire replacements.

But for knowledge jobs where it takes a few months just to get someone up to speed, you can see why hiring managers want to avoid hiring someone who is likely to leave soon.