What causes frames to break at the (rear) dropouts?
You already more or less answered your own question.

The reason is that in a freewheel hub the drive side bearing is close to the center of the axle. This gives the forces from your weight and pedaling much more leverage to bend the axle than on a Shimano-style freehub where the drive side bearing is located at the end of the axle. When the axle bends, it twists the dropout, which can also break.

Some other brands of freehubs solve the axle bending problem with a thick oversized axle. This could work with a freewheel hub too, but I am not aware of anyone who makes that kind of hub.