Why do we not yet have high dynamic range sensors which have the right exposition in every part of a picture?
There are already camera's with DR larger than the human eye, both instantly and overall. The human eye's dynamic range is not as large as most people tend to think it is. As I recall, it is somewhere around 12 to 16 EVs, which is right around the level of a modern DSLR.
The primary difference is that we have extremely natural aperture control that will adjust for different parts of the image. Effectively, our brains do image stacking for us automatically. When we look at the bright part of a scene, our pupils shrink and we see the detail of the bright portion. If we shift are focus to the darker part, our pupils rapidly open and we see the detail of the dark part. Our brain knows what the previous part looked like and so we don't notice the change in our peripheral vision, but we aren't actually seeing as much detail where we aren't focused anymore.
Similarly, even for the overall range of human vision, there are specialized cameras that can go far darker than us and still see, particularly color, they just are currently too expensive to produce for general public since they require very high quality materials and construction to get the noise floor super low. There are also sensors capable of looking at very bright objects that would be painful to people to look at.
Seeing is an active process
A big issue is that looking with your eyes is very unlike capturing an image - an image needs to include all information that the looker might look at, but normal vision is an active process that involves movement of the eyes, refocusing and dilation of pupils according to the objects we're looking at. Thus, if you want to capture "what the eye sees" you need, in essence, capture the viewpoint all the settings that the eye might use.
Your question is about dynamic range, but the same problem appears with visual detail and focus. A 'life equivalent' image needs much, much more pixels than your eye can actually capture, since the eye resolution is very unequal and while you're looking at only a single small spot with your high-res middle of retina, an image needs more detail available since you'll move your eyes. Movies need to choose a single focus, while a human can view a 'single image' with more depth by rapidly refocusing eyes and/or moving them for proper binocular vision at different intended ranges (e.g. looking at the surface of a window or through it), etc.
Part of the solution is exactly that - using a single camera multiple times quickly (or multiple cameras) to capture a variety of images at different settings and merge them afterwards, HDR is the most blatant example - just as our eye does, it actively looks at various different places with different "settings", and only afterwards your brain merges it all in a coherent picture or movie. The actual "images" taken by our eyes are already worse than good cameras, simply the mental combination of them is nice.
Your mental image is the product of not only the retina, but its interplay with the all the other components involved in vision, including the pupil and of course your brain. What may seem to you as a 'one picture' is in fact the result of high-speed adjustments and information processing and not a single snapshot.
You can find more information on this topic here.
It is entirely possible to make a light sensor with logarithmic properties - such a sensor would have incredible dynamic range at the expense of limited resolution for a particular exposure. Getting both requires a high resolution ADC. For CT imaging 24 bits linear is typically used - and then the logarithm is taken after offset adjustment to create the CT image.
A sensor that does both exposure control (integration time - think shutter speed) can do better, and if you allow changes in light collection efficiency (think f number) you get even greater flexibility.
Ultimate dynamic range is typically limited by readout noise - when you read the accumulated charge there will be some error - versus the largest signal that the electronic can support. As I said - 24 bits is common in medical imaging and that is better than 1 part in 10 million. That's a much higher dynamic range than the retina for a given exposure. But is is not commonly used in conventional cameras because the eye could not appreciate those details in the image - and resolution comes at the expense of speed.