Are we really unable to summon earth bridges? He still summons earth bridges in legion as well as in the sanctum of domination. It's more likely to be due to him not using his powers to take out garrosh.
But he's not feeling guilty. He talks about it with drake in korthia. He is assured by her that it's not his fault.
The internal thrall is split between whether it was his fault or not. He claimed that garrosh was the one to blame when he killed garrosh. He was devastated to learn that garrosh had caused him to go down the path to these choices. After the discussion with drake that thrall's spirit will return to his spirit-filled self.
Following the Assault on the Broken Shore, Thrall tells the Shaman and explorer that, ever since Garrosh was killed, he felt that Doomhammer was just a dead weight in him hands and that the Elements were no longer with him.