lm78xx zener diode
The real reason is that 780x (and similar) regulators are series devices, they are in line with the load and control the amount of current they let through so the output is maintained under different load conditions. You can think of them as being 'self adjusting' resistors that drop just enough to make sure there is the desired voltage after them.
Zeners, are shunt devices, they are wired in parallel with the load so they 'absorb' the extra voltage by dumping current to ground.
From a practical point of view, Zeners are not perfect voltage stabilizers, their voltage increases slightly as the current through them is increased and they are not very temperature stable. That can be a major issue if you just use them in the 'X and Y' scenario you describe. If your load changed from say 0.5 to 1.0 amps, in order to maintain voltage the current would have to be kept at 1.0 amps by sinking the unused 0.5A through the Zener. They obey Ohms law like everything else so:
Vz * (max I - Min I) can equal a lot of Watts.
Their place in the world is as voltage reference providers where some other element actually does the hard work, this is what happens in normal regulators.
Brian.