When/why would you use a Zener diode as a flywheel diode (on the coil of a relay)?
The current from the relay opening doesn't go into the Vcc rail at all.  It follows the path shown here:



The stored energy is dissipated in the diode drop and the coil resistance of the relay.

In the Zener diode configuration, the stored energy is dissipated in the full Zener voltage of the diode.  V*I is a lot higher power, so the current will fall faster and the relay might open a little faster:



MOVs are different than Zeners, but fulfill a similar circuit function:  They absorb energy when the voltage exceeds a certain level.  They are used for overvoltage protection, not for precision things like voltage regulators.