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I think originally, the rationale behind timing belts was that with OHC engines they did better. With a pushrod engine, the camshaft isn't all that far from the crankshaft, so the chain doesn't have to be very long. But with OHC, the distance is much greater, and chains were prone to stretching over time. The rubber belt wouldn't stretch, although it would usually act fine right up until the point that it snapped, so that's why they have service intervals. With a chain, I think the theory is that the car is wrecked or junked long before it starts to fail. Or, if the car is still running, it's old and worthless enough that the chain failure simply ends up being the final nail in the coffin, and you get a new car.

But, these days a lot of OHC engines have timing chains as well. My 2000 Intrepid, with the 2.7 V6 had a chain. I used to think it had two chains, one for each camshaft, but I just looked up a schematic and nope, just one long chain that goes from the crankshaft to both camshafts, as well as the water pump.
That thing looks like it would be nothing but trouble to me, although I had my car for 150,000 miles with no issues. I've heard in later years though that they WERE troublesome. Apparently, the guides would wear, and would allow the chain to stretch out.