Laws of physics
"Care to state which law of physics?"
Law of conservation of information. Which translates to a limitation the the amount of real information present in the image. Even with the best optics on the planet, the total number of photons arriving at any sensor scales with the size. If you halve the size of a camera, scaling everything, the sensor receives one quarter of the photons for each exposure. Sensor quantum conversion efficiency is pretty much fixed. The effective sensitivity (i.e. the ISO equivalent rating) is a function of the quantum conversion efficiency and the amplification applied to the sensor.
You can apply more amplification to get the voltages up before analog to digital conversion, but the raw information is not actually there. So you simply get more noise.
The upshot is that small sensors have vastly worse noise.
Cameras will apply noise smoothing algorithms - which is little more than blurring out the noise. They then try to sharpen the blurry image, which, in the end leads to a pretty unsatisfactory image. But one with a less obvious speckilng of noise. Typically these images actually holds less real information than a picture taken with a sensor with fewer but bigger pixels. If used in broad daylight it isn't so bad, just poor. But once you get into any sort of lower light situation, even just a cloudy day, it is not good at all. Indoors and it really starts to some unstuck.
In the end, the answer is easy. Bigger and fewer pixels. Accept that the correct design decisions should start with how the camera will be used, and how the results will be viewed. Poor light conditions and computer screens (or other camera screens) is the answer. This quickly leads to the conclusion that a similar sized sensor with one, or at most two mega pixels is the right design. Not a market driven design based upon an ignorant idea that more pixels is always better.