No "rule" exists prohibiting a pilot from deploying oxygen masks, but procedures do exist by which crews operate in any type of abnormal or emergency situation.
While a cabin oxygen mask does provide supplementary oxygen, it also combines the oxygen with cabin air...meaning that passengers who are drawing oxygen through the mask are also breathing in cabin smoke.
The masks can be prevented from drawing anything but oxygen...but they don't have a facial fit, knowledge of the mask is required, and the 02 supply doesn't deliver air for a complete breath; it's supplementary oxygen, to add to the cabin air that the passenger is breathing. That's all.
Oxygen systems come in different varieties. Some aircraft use chemical canisters which get very hot and generate oxygen. Others use oxygen stored in containers under pressure. If a cabin fire exists which is burning near oxygen lines, pressurizing the lines may provide an additional unwarranted hazard. Activating oxygen canisters may also provide an additional hazard.
Under some conditions oxygen will be provided, but under others, it will not. The abnormal and emergency procedures are written, and used, for a reason.