Disappearing Who

No, this post isn't about the Invisible Man meets Dr. Seuss. It's about the disappearance of the word 'who' at the beginning of a subordinate clause.

I often read or hear
the doctor that works at the hospital.
the child that plays in the backyard.
the father that cares for his family.
the mother that rocks her toddler.

But shouldn't it be
the doctor who works at the hospital?
the child who plays in the backyard?
the father who cares for his family?
the mother who rocks her toddler?

Shouldn't it be 'that' when referring to an animal or an object? Doesn't 'who' remind us, subtly I admit, that people, who are made in the very image of God himself, are of higher dignity than animals and things?

I'm probably reading too much into this linguistic trend, but by using 'that' when we should be using 'who', are we buying into the post-modern idea that people are of no greater value than the gum that's stuck to the bottom of my shoe?

SDG!