Image quality and possibly expense
Introducing yet another element in front of the sensor will degrade quality of the pictures, and for various reasons.
a) being outside of protection of the shutter will mean that it is constantly in contact with the air and dust. This will mean it will require more constant cleaning than a sensor would. How often do you clean the mirror inside your SLR? Hardly ever because you know it won't show up on photos. How often are you going to clean this extra piece of glass?
b) The placement of being between the lens and the sensor will mean that any dust on the glass would be spread over a larger area of the sensor, degrading quality. We probably all know what an example of dust on the 'sensor' looks like. That dust is on the protective glass right in front of the sensor, so only really covers the few pixels directly under. Being on glass in front of this would cause a larger smudge to be affected by the dust.
c) CA, diffraction, and all of those other nasty things. You have just had the light of your subject travelling through an expensive lens filled with precision glass. That nice white L lens you bought has scored amazingly well on sharpness and contrast tests. Now, however all that precision engineered light is passing at a steep angle through a cheap piece of glass placed in front of your sensor. Unless they spend a lot of money developing some very good quality coated glass, it is unlikely that it will not effect the quality of your photo. And depending on what lens you have, and the angles of incidence that the light from it is hitting this glass, will likely change how the glass effects it. To make none of this happen, you would need multi-element glass, or effectively another lens inside the camera, which would increase cost and give you even more to need to maintain and clean.
Also, in the placement where you put the glass, it might not fit with all lenses. I know some rear lens elements protrude more into the body with others, and I don't have any measurements, but at a guess some have been designed to only just narrowly miss the mirror as it flips up. Putting this glass in the way would mean these lenses no longer fit those cameras.
To summarise, it's not practical, and would degrade image quality. The sensor already has filtered glass on it that can be cleaned, and that is protected by a shutter that opens when it needs to to minimise contact with the air. Introducing an extra glass element removes this simplicity and makes the whole process of keeping things clean more difficult.