Atmospheric flight would definitely need this, but I wouldn't exclude its use in space missions for the sake of realism. At this point, I'd also say that speed of sound would boost situational awareness by adding the perception of distance to the perception of events.
Eyecandy and good gaming experience come before realism, anyway: this principle has been already applied to sounds in space, physics and many other things. Let's add something to the series. 
Mixing realism with Rule of Perception is just unnecessary. I can understand simulating doppler effect on the fly-by sounds because that just sounds cool and people expect it (thus, rule of perception).
However, as having sounds in space is far enough detached from reality, making the sounds have delays because sounds normally have delays would just be confusing logic. Having delays in the sounds like distant explosions wouldn't increase situational awareness or immersiveness because when you already breach the laws of physics to fulfill Role of Perception, then introducing this kind of pseudorealistic delays in space missions would just work to
counter that because people would not expect them.
In other words you would just have bug reports claiming that a lot of sounds are out of synch and delayed.
I have to say, though, that a fully articulating sound physics engine including speed of sound, doppler effects and sound barrier (have fun with singularities though - phear the div by zero!) would be magnificent resource for any atmospheric missions.
