On the other hand (just for the sake of discussion) lots of people have jobs for which they are overqualified. Barristas and taxi drivers with Ph.D.s come to mind, or attorneys applying for non-attorney jobs (we get lots of those).
I could argue that one either is or is not qualified for a job. If one's knowledge, skills and abilities exceed the minimum required, then one is qualified. There are many reasons why an employee might want a job for whch his or her qualifications exceed the minimum. Perhaps the employee doesn't want the stress of working in a more demanding position. Perhaps the employee has a spouse whose job pays much more so needs to find whatever he or she can get locally in order to support the spouse's career. Perhaps the employee has a medical condition that he or she doesn't wish to disclose but which makes it imperative to find a job that doesn't exacerbate the condition. Perhaps the employee is unemployed and desperate and willing to do anything. The employer doesn't know, and to really probe the true reason might involve asking illegal hiring questions.
If the employer is worried about how long the employee will stay, then the way to address this is contractually. There is nothing preventing a private employer from asking a prospective employee to sign a 3 year contract, for example. But employers don't want to do that because they want to be able to enjoy the benefits of employment at will. They don't want to be obligated to keep an employee they no longer need.
And of course the same is true of employees (although at the time of hire is when the employer would have the best leverage, i.e., a job that the prospective employee wants, to negotiate a longer term commitment if that is what the employer really wants).
It is a bit odd for an employer to decline to hire a qualified employee because of concerns about the prospective employee's commitment to longevity when the employer is unwilling to make a symmetrical commitment. If they are, then hand the employee a longer term contract, and if the prospective employee is willing to sign it, they have a deal.
I have, in fact, made this argument when I've served on hiring committees at my current job. I don't care for the argument that says, "We're going to pay this employee as little as we can, and promise them no job security, but we're going to expect them to make a long term commitment to staying in our job." In my opinion what that does is it guarantees that over time, you will be developing a workforce made up of minimally qualified employees who aren't able to get anything better anywhere else, or at least who don't believe they could. In my opinion that is not conducive to workforce excellence.