Channel separation in amps and dacs plays a role in how soundstage is perceived. How much of it we hear is a little debatable, I guess. With speakers, it is typically the delay (and volume difference as a result of the inverse square of distance) between the reverb and the original signal that creates the soundstage effect - or rather gives an impression of the size of the room. In the case of cased speakers (cabinet speakers? Idk what they're called), the size of the box will also affect the impression of size. With headphones, the 'room' ultimately becomes the headphone cup. In the case of closed headphones, it is simply a matter of reflections within the cup - which results in the typical "boxed in sound" (and obviously a larger sound when the drivers are angled (as it takes a larger number of reflections for the room reflections to get to the ear) and when the cups are made larger). With open headphones, the room is opened up - I'm afraid I can't explain the physics behind the reason for the larger soundstage in more depth than this, because I am not an acoustical engineer: at a guess, it is perhaps the reduced number of reflections, which makes the reflection seem further away because it is quieter (or maybe it's just the same as a large room, I dont know but it doesnt sound like speakers anyway). You also have other factors, interestingly, like treble response influencing how we perceive the soundstage. This is because the frequency response of our ear (particularly the treble) changes as we rotate around our head and the pinnae are struck differently. The difference in treble between left and right gives us a stereopositioning effect, which allows the brain to know where sound is coming from. Going straight into the ear has a reduced treble response - which is why many headphones have a boosted treble response - to mimick the sound of a speaker. A headphone that has a boosted treble response is more likely to seem coming from "all around" (diffuse field response), or indeed infront of the face (free field response), than a reduced treble, which typically sounds like it is very two dimensional (my experience agrees). At this point, you may notice that it is usually headphones that some consider bright - and certainly not those people consider dark - as well as those that are open, and have angled drivers (in some cases) that have a reputation of a large soundstage. Of course, this is a simplification and the angle the reflections enter the ear (previously mentioned) also creates some soundstage phenomena.
I'm afraid I can't comment on soundstage (or lack of) in balanced armature canalphones. I suspect distance from the ear also plays a role in soundstage effects but I can't articulate how/why.
As for why low-fi headphones have a poor soundstage well, I can't explain that one.