Actually, it's not totally impossible with iron sights. It just requires a hyperfocal focus with one's glasses. The focus has to be set at twice the distance from the rear edge of the front post to one's retina. Then, by a property of the hyperfocal focus, everything from half the hyperfocal distance to infinity is in an effective focus all at once. I have a custom set of a Revision Sawfly goggles with prescription inserts set up this way.
At the risk of bringing this thread far away from it's original topic, I did also want to come back to Guntuckian's comment about hyperfocal distance. It's certainly true that many competitive shooters, mostly those with presbyopia (all of us in the 40+ crowd), will at least consider a prescription shooting lens that is adjusted to focus on a spot somewhere close to 2x the sight radius away from our eye - the hyperfocal distance.
In theory this maximizes our depth of field, and allows both the front sight and target to be in reasonable focus. In practice I'm not sure the reality holds up to the theory. Remember that even though your prescription glasses give you a focal point set perfectly at your hyperfocal distance, your eye also has a lens, and it's not fixed. When you are firing a shot, and your eye is focusing on the front sight, the lens in your eye will adjust (change) your focal point to a point as close as it can to the focal plane of the front sight. The degree of this change will depend on many vision factors which are unique to each shooter, but I'm not sure it's realistically possible to take advantage of hyperfocal distance when shooting due to the fact that the lens in the eye will have a strong tendency to "mess up" your carefully crafted prescription.
In my experience what actually works much better is selecting the correct aperture. Selecting the right aperture will present enough light to the eye for good vision without eye fatigue, but will be small enough to maximize depth of field. Most younger shooters, for example, can get along just fine with an aperture as small as 0.38" in diameter. For me, while apertures that small gave a great sight picture and depth of field, my eyes would fatigue too quickly, and I've increased my aperture size to 0.46" with much better results. For comparison, it's my understanding that standard Tech Sight aperture size is .062" diameter, which is far, far too large to get much benefit from the aperture.
Once you get the right size aperture for your eyes, if you're shooting a service rifle (M14, M1 Garand, AR15), you can then if you wish get a set of match sights which include a small lens right in front of the aperture to adjust your focal plane even further if you wish. I am not using it currently, but I've run a +0.25 diopter lens in my AR15 rear sight with good results. Bob Jones sights, among others, has many different lenses available with different diopter settings (and even different colors).
My personal next experiment will be the use of the MISO sight system. This is fundamentally a very tiny Fresnel lens which purports to provide a multifocal capability that allows everything to be in focus, from the front sight to the target and everything in between. My initial examinations of it suggest that it seems to do exactly what it says it will do, but I've not yet installed it on my rifle to see if that holds up on the firing line.