Hi Electrix,
With a fairly stable unregulated input voltage, the current through the current-limiting resistor from it will remain the same with or without a load. Without a load and with the the current remaining the same, it has to go somewhere: through the zener to ground. 100% wasted current.
A shunt regulator regulates by shunting to ground any extra current that is not used by the load. If it didn't, then the output voltage would be equal to the unregulated input voltage because the current-limiting resistor wouldn't have a voltage drop.