If he can't change the timeline, he can only ( in theory ) interfere with the attempt to obtain information about the spread of the virus. And they can just send someone else to find that information. They're only limited by the number of Cole types they have at their disposal. If they send a "replacement time traveler X" who Cole knows nothing about, how much can he do to interfere?
How did the street preacher know Cole was a time traveler? Or the bum who called him Bob? There seems to be some kind of unexplained connection. That aside, someone uncontrollable who knows their methods, objectives and when/where they're sending people could raise hell with their operations. The scientist-council said they had had a lot of problems with unreliable time travelers. They were also shown to be a high-handed, demanding, controlling and not very ethical group, so eliminating those who don't follow their program to the letter didn't seem too far out of character.