Bleach Alone?
Stefve, As you said, I would not use bleach alone. I always use on most whites that can be bleached, as socks, dish towels, underwear, etc.
Dish towels and dish rags especially need to be bleach to kill the germs and whiten.
All I know is that when I hang my whites on the clothes line, they dazzle. We had a neighbor many years ago who did not use bleach, (talk about dingy whites??) oh my.