This might not seem like much of a question, but think about it. Without a tank, all DPS and healing players would have to pay attention to what's going on, and there would be room for things like distinct pulling, crowd-control, or burn roles. Without healing, survivability takes on a different role, and without DPS, groups become smaller and focused on a wider gap between tanks and healers.
Time is running out. What would the face of World of Warcraft look like with no tanks? What is Final Fantasy XIV without healers? If you could remove one role from the trinity, what would you pick?