The answer to every "why you should try..." question is: Because you just might like it.

If you need a power argument, do some raid parses with a group without a healer, then do some raid parses with a group with a healer and realize that the gaping difference between the two is a direct result of healer power (It has to be - you kept everything else the same after all).
The power healers have is pretty nuts, albeit largely invisible to the healer and it unfortunately can't be stacked either - more healers only spread that power among more heads, they don't add to it.

It's similar as with raise. On first glance, raise seems like a very bad spell, but it's actually hugely powerful, because the person raised would simply have zero further contribution if not raised and everything they do after being raised can be directly attributed to the raise and thus its power. Preventing people from dying in the first place works on a similar principle - Everything they do after the point where they would have normally died can be directly attributed to the heals they received. And like with raise being useless if nobody dies, heals are useless if nobody would die without them.

Still, with unavoidable damage, people are bound to die at some point and that's where healers cash in hard in the power department.