Personal independence is such an iconic American value today that few of us question it. In previous generations, retirees lived with family, but now that a large swath of older people can afford to live on their own, that’s what they choose. The convenience of digital devices means that we can now work, shop and pay our bills online, without dealing directly with other people. According to the U.S. Census, 10% of Americans work alone in remote offices and over 13% live alone, the highest rate of solo living in American history.

But...