That was my point. How does his interference matter if you can't change anything? Why is a time traveler going rogue a problem, when they can just send another one?
Even if they can't change anything, they can still learn and relay information back to the future. That's what the whole answering machine thing was about, and they even showed decisions being made because of it.
They're also all criminals (or something; I honestly had a hard time understanding what was going on in the future), and they have to know that they need to continue doing their job in the past or suffer the consequences (ie, having someone else come back to "correct" their behavior/mission). Else volunteering would not only be equivalent to being released from prison, but being sent to a relative paradise to boot.