How is wafer dicing economical (for small ICs)?

In general: Yes. You're losing area through the dicing street as the way the saw runs through is called.

However, your assumption of the thickness is wrong. The saw is more like a thin foil. Usually around 20 micrometers thick (factor 25 thinner than you assumed) and I've seen very specialized ones that were even thinner around < 8 micrometers. As a comparision: Typical bond wire pads (where the wires are connected to the Chip) are around 30-50 micrometers big. So your saw is thinner than the outer pad ring of the chip.

If you have a dicing saw in your hand it's kind of wobbely and does not very much look like a "saw". It is only able to cut the wafer because it is spinning at very very high speeds, which stabilizes the blade. The saws also have a very limited lifetime becuase of their small thickness. Usually they can only cut a few thousand meters before they need replacement.

There is also Stealth laser dicing, which has "zero kerf". The laser creates a tiny stress fracture inside the silicon, and the laser focal point is passed along the dicing channel multiple times at different heights within the silicon. Then the wafer is stretched, and the stress-fractured planes break. No silicon material is lost.

The kerf is not actually zero - the dicing street must be as wide as the accuracy of the laser positioning system, which is about +/- 5um (so the street is 10um wide).