It's about making the best of a situation that allows for it. We're using four microphones instead of two, which allows us to do things we otherwise could not do with just two. We can take advantage of that instead of simply duplicating what we would have done if we only had two microphones to begin with.
Most think of stereo as being mostly about left/right. After all we are recording left and right channels most of the time. Point one mic left-ish and one right-ish. Yet a deeper and more fundamental aspect is the balance between direct-sound/reverberant-sound. And even at the level of left/right-ness, there are are other equally important stereo aspects such as the sense of width, openess, center/side-ness, etc.
Omni microphones are often considered to sound natural and open compared to directional microphones. But it can be difficult to use them optimally because we have no control over directivity and recordings made with them can sound distant, muffled, boomy, etc. unless we can put them in the optimal spot in an optimal sounding room. By using more than two directional mics and arranging them in such a way that the combined coverage of all of them together approaches omnidirectionality, we get a very natural, open "you are there" type sound but with directionality. We gain control over left/right/front/back/side-to-side balance of things in ways we can't using just a pair of omnidirectional mics or just a pair of directional mics. It gives us some control and differentiation over direct/reverberant, front/back, left/right, and center/sides, with improved left/right imaging as well.
Here's an analogy which might help-
Consider a two channel Mid/Side microphone setup. The Mid microphone faces directly forwards and records the up-front mono component of the sound- ideally dominated direct sound from the stage and PA. But the Side microphone faces sideways, recording the stereo ambience and width components of the sound- more or less everything except the direct sound coming from directly forward. It wouldn't work if the Mid and Side microphones were both pointed directly forward.
The PAS Neumann pair (X/Y or near-spaced) is analogous to the Mid microphone, focusing on the direct sound from the stage and PA. It just has some added stereo directionality to it. The sideways or backwards pointing Naks are analogous to the Side microphone, recording the spatial aspects of the sound, basically focused on everything else except the direct sound. The Neumann pair then does it's job best partly by excluding most everything except the direct sound (thus PAS), and the Nak pair makes it's contribution partly by excluding the direct sound and maximizing the ambient difference signal (thus pointed 180 degrees apart to maximize the difference between them, or directly away from the PA to minimize the direct sound pickup as much as possible). We get some control over the direct/reverberant balance by how much of the Nak pair we mix in with the Neumann pair, similar to adjusting the Mid/Side ratio of a M/S pair, but we have much more flexibility in doing so, and other stereo aspects like left/right and mono/wide can be addressed and adjusted separately.
The better sounding the room, the more leeway we have to not focus on the direct sound alone, and the more open natural and convincing the recording will sound. In a crappy sounding concrete box music club we might need to try and exclude everything but the direct sound as much as possible just to get something decently listenable which isn't all mud, boom and reverb. But in a good sounding space there is no reason to sacrifice everything else. Outdoors we are free of room problems for the most part, so setups which record in a more overall omnidirectional way (in a well managed omnidirectional way, determined by how we point and space the directional microphones) can make for much better recordings which we can't make in lesser environments.
Sure you can use the same microphone setup outdoors you'd use in the concrete box club, and it will probably sound somewhat better, but the point is that it could sound a whole lot better! I look at this the other way around-Figuring a setup appropriate for a perfect acoustic is my starting point. Figuring a setup used for crappy music clubs is a modification of that, doing whatever is necessary to make a good sounding recording in a non-optimal situation.