But that is not how Kaladin has acted anytime something traumatic has happened to him, when he watched Tien die he got out of line, screamed at him and ran towards him. When his unit in Amaram's army got killed after, he got into the fight and killed the shardbearer, same with bridge four. And he did not froze, he chose not to act, the book is specific,
"Kaladin screamed, tears streaming from his eyes. He begged them to just stop, to listen"
He screamed, he told them to stop, he cried, he just did not act, he did not try to protect anyone, he just gave up. This is the only one time he does not act. I dont beleive is consistent with the character of Kaladin, he has lost many people before in as traumatic or more events, and realistically (at least in the real world, the first trauma event is the one more likely to freeze you) he should have tried to stop the fight, physicaly, as he has done in any other instance, not using lethal force, granted, but tried nonetheless even if it was futile, because that is what how the character of Kaladin was portrayed on the 3000 previous pages.