It's true Natasha is supposed to have some vile history, but even in the present she's nearly an anti-hero and that's how she fits in. She came to SHIELD after her dark past was behind her.
Ward has no place with the team after what he's done. If SHIELD still existed and somehow took him back as an agent, there's no way the characters on team Coulson would accept it or stand in the same room with him. Too much personal betrayal.
Coulson *almost* threw May under the bus just for lying about reporting to Fury, someone Coulson doesn't consider the enemy. Coulson would probably struggle with the desire to outright shoot Ward between the eyes for his crimes, not the least of which is murdering Victoria Hand.
Edit: though it seems clear Ward is living with delusions about his actions judging by his arguing with Skye. I could see him doing the heroic sacrifice, yeah. In fact, that may be his only way out. He can't come home, and Hydra will eventually use him up and throw him away.
