The manufacturers did this to themselves. They started making belts using natural rubber as the matrix and natural rubber does not age well. Once the rubber starts to deteriorate, the reinforcing fibers become delaminated and the belt breaks.
Newer belts use a urethane rubber that lasts much longer, but still eventually cracks and allows the fibers to delaminate. If they used a silicone rubber, the belts would last the life of the engine easily.
The belts could also be easier to replace. I had a 79 Dodge Colt with the 1.4 Mitsubishi engine, changing the timing belt was a 20 minute repair. The later Mitsubishi 1.5 engine in my 90 Dodge Colt was much more difficult to change, but no where near as hard as the belt on a Honda.
From the manufacturers viewpoint, in the late 70’s when timing belts started to be used, most new car buyers only kept their car 4 years, and the timing belt lasted 4 years so the manufacturers customer, the one they made money off of was not affected by the cheaper belt.
As people started keeping their cars longer, the manufacturers had to make the belts last longer so they upgraded the materials. Some also got their dealerships to offer a special price on the timing belt package as Honda did so it didn’t seem so bad to those customers that kept their cars past the belt life,
Now, new car buyers are keeping their cars an average of 11 years. This may drop in the next survey but the recession was the reason that people were holding on to their cars longer. They could have gone to silicone rubber belts but those are really expensive. If the chain will last through the 11 years and costs less than a belt, then that is what they are going to do.
The chains used on an OHC engine are not the heavy duty, multi row toothed chains used on the old iron block V8’s of yore. They are more like bicycle or motor cycle chains. Some are double row and will last forever it seems like, but more and more, they are going to lighter duty single row chains. We shall see how these hold up.