I find the whole idea of interns completely absurd in the first place. What is wrong with giving a beginner a beginner's job with beginner's pay? They learn on the job, acquiring experience directly related to the company, service, whatever where they are working, increasing their value and the pay over time. That's how it was when I left university and when M absent left school and it seemed to work okay then.
However, assuming that young people are stuck with this daft idea instead of a proper job, I am fairly doubtful about old people offering low price accommodation in return for help. Having had resident nannies, au pairs, etc. I quite treasure having my home to myself these days (with Mr absent) and, although I miss absentdaughter, I don't think I'd want to be sharing my house with her. I'm not frail enough – or at all– to need someone to help me, but if were, I think I'd feel a bit vulnerable and anxious about having a complete stranger living in my home.
I would also be concerned about the young person's boyfriend and other visitors for whom, of course, a company could not vouch.