You are absolutely right -- completely white sectors on leaves don't photosynthesize, and plants that produce whiter leaves are going to be inherently less vigorous than ones with green leaves. So why are they like that?
Most variegated plants are essentially man-made -- they are unhealthy, mutant freaks that would die if we didn't like them and keep them alive in our gardens. Sort of like chihuahuas (except chihuahuas are disgusting and variegated plants are delightful.) Surprisingly, however, some wild plants, like some caladium, begonia, and dieffenbachia naturally have white patches on their leaves. Breeding has increased the amount of white on the plants we grow, but still, the wild plant have distinct white patches on their leaves. Why?
Because they are liars.
Imagine for a moment that you are a expecting mommy-to-be leaf miner. You are flying about, looking for a good leaf on which to lay your eggs so your babies can happily start eating away at them. First you see a leaf like this:
This looks perfect! You land, and lay some of your eggs, and then happily fly on to find a home for the rest of your brood. But the next leaf you see looks like this:
In other words, natural leaf variegation is the plant equivalent of pretending you have whiplash in order to get insurance money. This is a fact that should make those of you who don't like variegated plants because they look unhealthy rethink your position. That is just what those plants WANT you to think! You are being fooled, just like the little leaf miners. Go buy some today just to show those plants you are smarter than them.
If you want more of the science behind white leaves, here are some good papers (subscriptions required):
The history of research on white-green variegated plants
Ecology of a leaf color polymorphism in a tropical forest species
Leaf variegation in Caladium steudnerifolium (Araceae): a case of mimicry?
Have a question? Get a sciency answer! Just e-mail me: engeizuki at gmail dot com