You can normally “see” your rear aperture, your front sight, and the target at the same time. The issue is that normally only one of them will actually be in focus. The other two will be visible but blurry. This is due to your eye’s depth of field. With any lens system, when you focus on a particular object some things in front of it and some things beyond it will also appear to be “in focus” (I put “in focus” in quotes since the term actually depends on what resolution you mean when you say in focus, for shooting purposes it is general not as fine as if you’re doing macro photography) but most things in front and behind of what you’re focusing on will be out of focus. The closer an object is to the lens (your eye in this case) the shallower your depth of field. For example, on a rifle if you focus on your rear sight, your depth of field will be quite shallow, maybe an inch in front of the sight and a couple of inches beyond it. So your front sight and target will be out of focus. If you focus on your front sight, your depth of field will be bit deeper, but still only a couple on inches in front of the sight and maybe a few feet beyond it. So your rear sight will still be out of focus as will the target. If you focus on the target, if it’s beyond say 100 yards, you might be at your eye’s “hyperfocal distance”, which means everything beyond the target will appear in focus, but both the rear and front sight will be out of focus.
This is why you should focus on the front sight. While your depth of focus will not include the rear sight and the target, everything will be closer to being in focus range than if you focused on either of the other two.
While it’s true that being able to rapidly switch focus between the three objects can make targeting easier, you really just need to concentrate on keeping the front sight in focus. The rear sight will be blurred, but that’s the advantage of a peep sight. Even if the edge of the peep is blurred, the center opening will still be a round hole that you can center the front sight in. You actually never focus on the hole, you just look through it. And while the target will be out of focus, it should be on the far edge of your depth of field when focused on the front sight and be good enough for you to recognize the bull.
Another thing that will effect your depth of field is your pupil size. The smaller your pupil is open, the deeper your depth of field will be. That’s why you never want to wear sunglasses when using irons. You want your pupils to close down as much as possible to increase your depth of field.
That’s the big advantage of optics. With a good optic you can adjust it so that the sight (reticle) and the target are all on the same focal plane so that everything can be in focus at the same time.