If you get it right -- don't flip the phase of the signals, use appropriate microphones, and get good levels all the way through, record to a really good medium -- you can get amazing results.
If you are certain that the music will be played back through headphones, you can embed two mikes in a mock-up of a human head -- better yet, inside the ears, and require playback through in-ear monitors -- and get an amazing sense of realism.
That's not the way most music is produced these days, though. That's like a single-author software project with everything written from scratch: there are some, but not many.
Music is rarely made in real-time at a live performance. It's usually made in an editing suite after dozens, hundreds or even thousands of individual recordings, samples and synthesized effects are made, gathered or licensed. These elements are brought together, altered, fused, and made into a final bitstream that represents the producer's best effort at realizing their musical intent.
You can get amazing things out of that process, too. Works that could not reasonably be made any other way.
However, in that workflow, the original real world spaces in which the source materials were made -- if any -- are mixed and lost. To produce stereo in a two-channel final recording, many tracks are simply assigned to one channel or both channels at specified volumes. This loses or confuses phase and delay information that humans use for spatial location.
The crossfeed filters are another post-processing step, this time in the hands of the audience playing it back, that can simulate some of that spatial location information. It can do this to a greater or lesser degree; the more information available at the beginning of the process (about spatial location), the more can be introduced.
Eventually we might see artists routinely producing multiple final products, some of which have been rendered to virtual spaces for headphones or IEMs, others being set for surround configurations or stereo playback. Better software tools will help with that -- a scriptable 3D GUI that places your virtual instruments and virtual audience in a virtual ambience could be immensely useful.