There is another factor to consider: temperature.
When air is laminated in the valves of first and second stage, the enthalpy of the compressed gas is substantially preserved. As air is quite close to a perfect gas, ans isoenthalpic expansion results into an isothermal process.
So the temperature of the gas does not drop significantly, just a few degrees due to the Joule-Thompson effect (caused by the fact that air is not exactly a perfect gas).
But if, during the expansion, you convert part of the initial enthalpy to mechanical work, instead of dissipating it into heat in the lamination process, at the end of the expansion the remaining enthalpy of the gas will be much smaller than the enthalpy at the beginning. And hence also its absolute temperature will be reduced significantly, dropping way below the freezing point. This causes a lot of problems, the regulator can easily be locked in free flow by the ice.
For cold water diving, regulators are usually designed for getting a pressure reductoin almost isothermally.
Converting this to an almost adiabatic expansion is truly a bad idea, as the resulting gas absolute temperature can easily become half of the original one, if half of the available energy is converted to electrical energy.
So if we start at 300 K (27 °C), the temperature will drop to 150 K (-123 °C) causing everything to freeze, and making the gas not breathable.