When the Master dies, the Servant no longer fights in the Grail War. Tohsaka said that they could kill the Servant, but it is a lot easier to kill the squishier Master.

Emiya is...chivalrous. He doesn't want to put Saber in danger if he doesn't have to. Saber is still hurt from the Berserker incident, even if it doesn't look like that. He still has illusions of hero-dom.

There's a lot more to him than they've shown so far.