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Why is a stereo file created so that the vocals are present at an equal volume in both the left and right channels, while instruments are louder in either the left or the right channel?
I.e. what is the purpose of creating such a stereo file?
Note that this kind of stereo files allows us to cancel vocals by inverting a channel, but I don't think it is the purpose of creating such a stereo file.
This is just a very popular stylistic choice made by mixers. When mixing most music, the most important parts are usually emphasized, which means they are usually mixed louder and clearer. Because of the way our brains interpret audio, we perceive sounds that appear to be right in front of us as the most important ones, all other things being equal.
So the most important parts of a band are usually (not always) mixed in the center. This typically includes, vocals, bass guitar, kick drum, snare, and any solos that are played. Note that other drums, backing vocals, other guitar parts, etc. are usually mixed more or less to the sides to "make room" for the important parts in the middle, as well as to create a more interesting overall picture.
It's worth mentioning some exceptions to this popular practice. Classical symphonic, chamber, or other ensemble music is almost always mixed to recreate the live experience, regardless of anything else. So with a recording of a symphony from the classical or romantic periods, the first violins and the concertmaster will be mixed on the left side and close sounding, cellos and basses on the right, brass and tympani farther back and a little to the right, etc. Even if the concertmaster or another instrument has a solo, their placement in the mix will not be changed, although a spot mic may be used and brought up in level to make sure the part stands out a little bit.
Some mixes of Beatles recordings were re-done in stereo on a console that only had hard left, center, and hard right panning, so the entire drum and guitar parts might be on the left and all the vocals and bass parts might be on the right. This is why many Beatles fanatics prefer the mono mixes.
On The Downward Spiral, by Nine Inch Nails, some of the songs are mixed in unusual ways. In one example, the lead vocals are muffled, panned hard left, but made very loud in then mix.
To create stereo separation and use your entire sound field while keeping the dominant part of the music centered so that your not "pulled" to one side of the stereo field. It gives everything it's own space so that you can hear individual instruments but still stays together. Certain times or in some genres it can be used to simulate the natural positioning of the musicians.
