First of all, note that supply has dramatically decreased along with demand (though not quite as dramatically). As an example, United Airlines is cutting its May schedule by 90%.
Second, given the very strong advice from government and expert sources that people should avoid non-essential travel, the population is now, roughly speaking, divided into two groups:
Those few who absolutely must travel, and will do so if they can afford it at all;
The majority who do not need to travel, and would not (or should not) do so, no matter how cheap it was.
Lowering prices might pick up a very few extra passengers from the first group, who urgently need to travel but can't quite afford to do so at the current prices. But it would do nothing to increase demand among the second group.
In other words, demand for air travel is now highly inelastic; demand is not much affected by price, and even a large change in price would likely have only a small effect on demand. If anything, airlines would probably find it more profitable to raise prices right now, because people in the first group would probably be willing to pay more. But they likely won't do this to a great extent as it would look like price gouging, and might look bad to the government officials on whom they're depending for bailouts.
Third, and related to the previous point, even if the airlines could somehow raise demand by lowering prices (or advertising or other means), that increased demand would have to come from non-essential travelers. If the airlines are socially responsible, they won't want to do anything that would encourage people to travel unnecessarily. And even if they're not socially responsible, they probably don't want to present the appearance of doing something socially irresponsible, either to the public or to the government (see above).