Orbital Habitat

Long ago, the mathematician Joseph-Louis Lagrange found that for any three-body orbit (that is, three large objects, a la a solar system), There are five points where you could introduce a new object and its orbit would remain stable. The next paragraph will review this idea -- feel free to skip it if you are a mathematician, physicist, or computer scientist.
The points are numbered, L1 through L5. There are two existing bodies, one larger and one smaller. For the purpose of this exercise, we will call the larger body "the sun" and the smaller one "the earth," although this could easily be adapted to any solar system. L1 is directly between "the earth" at a short distance past where the moon orbits. A solar probe is in fact maintained at this position, because it's really useful for studying the sun. (It stays with the earth's orbit, has a direct, unobstructed view of the sun, and so on.) L2 is on the other, night side of the earth, and would be a great place for a deep-space telescope. It would move with the earth, and remain forever in the earth's shadow, seeing deep into the darkness for a great resolution. (Apparently, someone else beat me to that idea, because two probes are already there, and three more are planned.) L3, L4, and L5 are the most interesting ones for this. L3 is on the opposite side of the sun from the earth, in the earth's orbit. L4 is 60 degrees "ahead" of the earth, L5 is 60 degrees "behind." The Lagrangian points are maintained by gravitational balance, and will stay in relative position until pushed out by some other force. Math, it works.
I think we should build habitats in L3, L4 and L5. They could have polluting factories, dangerous crops, or just people who we don't want anywhere near the earth. (Like say, the chronically annoying.) The platforms wouldn't touch Earth, would have an excellent supply of solar energy to power industrial or agricultural activity, and would survive events that would destroy the human ecosystem. (Oops, we nuked ourselves out of existence? L4 can reseed....)
This would be insanely expensive. Cheaper than terraforming mars or venus, but still in the multiple billions, and up to trillions, especially if we make it a large, human habitable habitat, and not just a simple lightweight probe.