I often hear that tanks or healers are more "important" in raiding. But I disagree. I think it's an illusion. And it works like this: A healer can wipe a raid almost instantaneously. A tank can similarly do the same. But a dps can in the long-term do it by being low in damage and eventually reaching an enrage. Sure they are more but collectively they will do it. A team with high dpses will make it easier for healers and tanks. There are encounters that the healers have it easy when the dpses are good since the encounter never reaches certain soft enrages. Also a healer can be helped by other healers. Tanks and also healers are often "alone" and that's a good argument (a dps can be compensated by other dpses) but that is not true when one goes to more complex encounters. The hardest the content the more important the roles of dpses. In fact there are encounters that the dpses might have more important jobs that the healers and the tanks. This is often seen in complex end-bosses of heroic mode, for at least some of their phases. Additionally certain particular dpses might have special important jobs that overcome the importance of a tank or a healer. In practice, certain tanking encounters are very easy, just a tunnel vision and a rare DBM-assisted hit of a cooldown. Also some healing jobs are easy, e.g. tunnel visioning the healing of a tank in a rotation one just does automatically.
tl;dr: In most introductory encounters dpses do seem less important but when one advances into harder content the whole raid becomes important. In certain special jobs, some particular chosen dpses have more important jobs than anyone in the raid, in others tanks or healers might have it easier. It is unfair to call any of the 3 roles 'easy' or not. (and we could separate dpses into ranged and melee but it wouldn't make much of a difference since they are often put together in this fallacy)