He only takes crap from Geralt because he needs himI don't think that Emhyr is the kind of person that kills people over a hissy fit, at least that is not how he described in either the books or the game. He takes a lot of lip from Geralt and doesn't even really go after him if Geralt continouly refuses to bring Ciri. That doesn't mean that I think Emhyr is kind, he is cold and precise and deals with people like one would with a tumor: Cut them out before they do too much damage. I am not sure what harm Letho, a lone witcher, could do either to his person or his reputation.
Book!Emhyr isn't an idiot or a weak leader, if he was he would have just stayed the figure head of the group that put him on the throne in the first place. Instead he became one of the most respected and feared names in the continent's history. Game!Emhyr is a backdrop, little more than a well-executed character in a film noir story, that gives Geralt the impetus to look for Ciri.
Emhyr: You are insolent because you believe I can not touch you. And you are right... For the moment. But the day will come when your usefulness to me has run it's course.