Dont be too concerned about phase unless its very severe and causing problems. The fact is, like mentioned above, their are phase problems in everything. Infact phase has alot to do with sound in general. Phase cancellation can also be created from things being out of tune. Its a different sound generally but it is phasing that makes us tell if things are out of tune or not. And when things are in tune, it makes the instrument bigger. Think of an orchestra, when you have 20 violins or more playing at one time, the same thing, theres no way their frequencies are going to be in phase. Thats what creates the orchestration effect. Then you have everything in its own register, and distant creating its own phase sound.
Without phase there would be very little stereo imaging in general. Our ears localize things by difference in time that it hits your ears. Thats what stereo imaging is.
I dont think its more important that the high frequencies are inphase than the lows. Both can give the same amount of problems. But the thing is, its alot harder to hear the problems in the highs when they are out of phase than the lows. Its obvious when bass frequency cancels out, because its a complete dropout. Thats what causes the loss of volume. then you still hear the highs but they sound combfiltered instead of just gone.
This is also why it is recommended to do X/Y Stereo micing instead of very spread A/B in alot of situations. Think of a drumset. You have them spaced 3 or 4 feet apart, then the phase is completely different from the left mic to the right mic. This is what is giving it a very wide spread. But what if the snare mic is 180 degrees out of phase with the left mic, but completely in phase with the right mic. You notice this during tracking and do a polarity reverse on the snare mic, now its just reversed but you still have the same problem but its in the right mic now. So based on this theory, theirs no way to get the snare mic completely in phase with the overheads, because not even the overheads are in phase with each other.
This can work as a good effect if you spend the time to get it right. But you will lose alot of the tightness in the whole drum mix. But with X/Y where there are very minimal phase problems because the stereo is based on amplitude levels. Then you can much easier get the snare mic perfectly in phase with the over head mics, which will focus the sound and make it larger. But you wont have a wide stereo feild.
This is why a 3 mic technique with kick and 2 overheads is a good idea for those who cant recognize and fix phase problems. Its a really big deal in these kinds of applications, and most likely you will get a better sound by using just 3 mics.
Danny