Here's my thought about that. If they take your offer because they're having a hard time finding a more senior job, it won't suddenly get easier for them to find a more senior job after you hire them. So I think this risk may be overblown.
> it won't suddenly get easier for them to find a more senior job
My experience tells me otherwise. As soon as you have a job, everyone wants to hire you. If you have no job, nobody wants to touch you. It's kind of like dating, where scarcity makes you attractive.
Sure, but the 'overqualified' person is going to be job searching from day one. The alternative might say a year or two to grow and then look for something better.