When he was young, Frank stopped training to become a priest because he couldn’t forgive guilty people for their sins. He’s a man that believes terrible things you’ve done must be worked off through your sweat & blood. And obviously the same principle would apply to himself. I’ve always believed that Frank refuses to be with his family because he hasn’t forgiven himself yet for killing them/letting them die. He asked for a war, he has it, and now he’s waging it until either crime ceases to exist or the day he dies. So it’s a case of “Who punishes the Punisher?” Answer being “he does, every day of his life.”

Of course, I can’t keep up with modern comics & I therefore haven’t read this one. But your hypothesis is a fine one as well.