There are a number of factors in play which correspond to the perception of distance or proximity in a recording and the microphone setup used- change in timbre with distance, change in stereo image width, change in the ratio of sound arriving directly verses by way of diffuse-arrival paths, differences in phase-correlation with angle of arrival, etc. Presumably the intent is to get a recording made from a distant location to sound like it's closer than the position in which it was actually made, or at least reduce the perception of overly "far-away-ness"
Timbre-
Unlike directional microphones, the response of an omni doesn't change with distance from the source, so it is already ahead on that account. And outdoors there is no issue with room size, modes, reflections and that kind of muddiness which can compromise the usefulness of a distant pair of omnis indoors. This is why a pair of omnis makes for an excellent foundation for distant outdoor recording. [edit- some midrange "presence" EQing is often the secret sauce with distant omnis]
Image width-
The farther away the recording position is from the stage/PA, the smaller the apparent angle between the two PAs and outer edges of the stage as viewed from the recording location. Because of that, as the recording position is moved farther and farther back, the spacing between microphones needs to be increased at the same time in order to maintain a similar apparent stereo image width between playback speakers. This applies to microphones of any pattern, not just omnis. Directional mics can be angled less far apart to achieve a similar effect on image width to some extent, but require an increase in pattern tightness to maintain sufficient differentiation between channels as the angle gets more narrow, and rapidly exceed the limit unless the spacing between them is not increased at the same time. A larger A-B microphone spacing may worry folks due to the possibility of a "hole in the middle", but that becomes less and less of a problem with increased distance from the primary source of interest. At more distant recording locations, more spacing can be used before the imaging for sounds arriving from either PA or stage edge extreme are pulled fully over to one playback speaker or the other. And if using an 3rd mic in the center, or a properly arranged pair, or three, or four, there is no worry about a hole-in-the-middle.
Change in the ratio of direct-arriving verses diffuse-path arrival sound-
From a close enough recording location pickup pattern can affects this, but can't do much about this from a distant recording location other than moving closer.
Phase-correlation with angle of arrival-
We should probably stay focused on the other aspects and forget about this one! It is also related to the spacing between microphones, yet more in terms of coherence and time-smear rather than in terms of left/right imaging. Sound arriving perpendicular to the microphone elements in the array will have tight phase-correlation while sounds arriving from increasingly off axis will have increasingly different times of arrival. This has a tendency to portray the on-axis stuff as clear and sharp across the entire frequency band and the off axis stuff as more diffuse. With lots of microphone elements in the array we get a phased-array beam-forming antenna like effect. How many? Although it probably doesn't correspond closely to antenna array theory using only a minimal number of microphones as discussed here, it certainly seems to be in effect to some extent in my listening. Consider it as relating to the "big sound" of spaced omnis with regard to decorrelated reverberant and ambient pickup (non-perpendicular arriving sound), while achieving correlated pickup of the perpendicular arriving sound, but with potential increasing comb-filtering issues as additional elements are summed together. [edit- I currently use 5 microphones (technically 6 if you count the side-channel of the center Mid/Side pair) for pickup of sound from the front in my big rig, and can hear what I believe to be a rudimentary form of this when listening while muting and un-muting some of those elements]