Obviously there cannot be just one homeless chap. Homelessness
is a problem because it indicates the absence of shelter, a basic
human need. White hair indicates no absence of any need on the
other hand, so your analogy is invalid.
But anyway, it is not so easy to get people to open their homes to
someone. Solving homelessness does not just include providing a
roof; it also involves paying for that person's food, water and
transport consumption, not to mention healthcare bills (which are
rather high). As it happens, my domestic finances are rather tight;
I cannot afford to house someone else. And I'm from the
middle-class, which likely means that most heartlanders porbably
cannot take on an extra family member.