One of the issues with trying to emulate human sight in a photograph is the field of view.
The perspective we see, which is a function of relative focal length is by most accounts roughly the perspective of a 50mm lens on a full frame sensor or 32mm on a DX sensor, but then the problem isn't perspective, it's field of view. Think of the picture you see at 50mm and now extend the field of view such as you would when taking a panorama.
If you took a "human" photograph, you would see almost 180 degrees horizontally and approximately 120 degrees vertically, yet still maintain the perspective of the medium focal length.
Take this crude diagram of the eye (green) and a digital SLR sensor (blue). You'll note that the focal length is exactly the same for both mediums, 17mm approximately, but the angle that the retina extends round to is much more than that of the sensor.
It sees a larger field of view, with the same focal length. This is why a DX sensor equates to the field of view 1.6 times smaller than that of the 35mm sensor, yet at the same focal length, the perspective does not change. It simply captures a smaller area of the scene.
Panoramas are a way of emulating the field of view of something like the human eye whilst retaining the flatter and more realistic perspective.
The next issue is dynamic range. An average dynamic range of digital SLR sized sensors is roughly 11 stops of light. This means it can record the difference between 11 doublings in light intensity. 1, 2, 4, 8, 16, 32, etc. How accurate is another story. 14-bits is better than 12 and 12 is better than 8 bits, but analog is even better than 14-bit digital.
Whilst a full frame professional body capable of capturing up to and over 13 stops on a good day is considered impressive by modern standards, it doesn't even come close to the human eye.
The human eye is at times capable of distinguishing the difference between roughly 18 to 20 stops of intensity, in a very crude measurement. This means that the black shadow that your camera sees could be quite easily seen in detail by the human eye, at the same time as seeing bright details in the scene. This is where the dynamic range of a digital sensor currently falls down.
It simply cannot distinguish such wildly different light intensities at the same time. Sometimes it's so bad that you have to either expose for the highlights or expose for the shadows and suck it up, even when your own eyes can see both fine.
HDR is a way of emulating the dynamic range of the human eye, but is still limited by the mediums on which it is viewed as well as the way it is processed.
Another issue is that whilst it's a walk in the park for us as our brains are designed to see this way, only the fovea sees in great detail. Peripheral vision is rather undetailed, and is primarily there to see motion, which can help us identify that things are happening around us or warn us of danger and trigger the fight or flight response.
If you were to simulate this in a photograph, the image would have a small in focus area in the center and the image would quickly become blurred as you move toward the edges.
There are other issues which I have either not touched on or do not know about myself, but I think at the end of the day, a photograph is not really meant to "emulate" the human experience, it's meant to capture a moment, to create a response or an emotion, or to capture memories, or to get a big paycheque from a client :)