It's very important to realize that it is not the high ISO setting itself that results in noisy image, it's that fact that using a high ISO setting means you capture very little light.
Light is made up of photons which are randomly emitted by a lightsource. When the light levels are low or the exposure time very short then the number of photons you get will vary considerably from
Imagine you are trying to estimate the rate at which people are leaving a shopping mall. If you only have 10 seconds to count people then the result you get will vary a lot depending on exactly when you start counting, and which exit you chose. If you have 10 minutes to count people, then you will get a much more stable answer which will be similar for all exits (assuming there is no personal preference for exits) and across different 10 minute time windows (assuming there are no other factors influencing the result).
That is what is happening when you use a high ISO setting, you capture very few photons so a set of neighboring pixels covering an object of uniform colour might receive 4, 3, 4, and 5 photons each, so instead of a smooth uniform colour you get a grainy result that changes for each pixel.
This noise is called photon noise and is the dominant source of noise in high ISO images except in the shadows. Even if you had a perfect sensor that counted and faithfully reported each photon that hit the sensor you would still have a significant amount of noise in low light.
That's not to say that we have reached the limit of high ISO performance. Not quite yet any way. Pure photon noise is very fine grained is less objectionable than the clumpy pattern noise observed in high ISO photographs.
Reducing pixel cross talk, improving the electronics in general might only have a small effect in reducing noise amplitude, but a larger effect on improving noise quality.
Wikipedia has a simulation of the "perfect" sensor where photon noise is only noise source:
Click for a larger version where you can make out individual pixels. Image by Mdf some rights reserved.