[EricVanWyk]

For the FM bands, you can probably get away with it. A hacker EE can get all sorts of ugly to work (for some duration of work). But, why bother when the "right" solution is just as easy / affordable?
The first thing my RF mentor ever told me was "RF is the easiest of the EE disciplines as long as you do it right and don't screw up. Once you screw it up, thats when it becomes FM*".
Basically, you don't want to add sources of error that are avoidable. The potential problem with a resistor + zener instead of a linear regulator is output impedence / load transients. In other words, the actual output voltage is now a function of its load. This effect can wreck the linearity of a system, and cause distortion.
Imagine an output amplifier that is supposed to double the input. That is, out = in * 2. For most RF amps, what it actually is doing is out = in * constant * power_rail. If power_rail depends on out, you get something on the order of out = in * constant * power_rail + in^2 * other_constant. This usually isn't a problem with slower amplifiers, but those will still have a power supply rejection ratio that isn't perfect.
This is partially why RF circuits have way more bypass capacitance than usual and why so much effort is put into ensuring the integrity of power and especially ground.



*FM actually stands for "freaking magic", not "frequency modulation". This describes both how FM radios operate, and the occult chicken sacrifices necessary to make an EMI problem go away.