Carol was right: anyone infected to that degree dies and reanimates.
Carol: took it on herself to go ahead and kill people because she decided it's better to just give up.
What did Hershel do as he passed one cell after another with increasingly sick people? Caleb balked at Hershel's conern, as he realized what was happening. Did Hershel think he was going to save them all--with no clue about the whereabouts of Daryl's party?
What did he tell Rick they should do with the bodies? Burn them--a logical solution Carol reached before anyone else.
There's no time to play games with the inevitable.