Details will vary between different displays but my point is that due to the pixels being on a grid sequential access is going to be faster. This is not unlike memory.
EDIT: Here's a reference that discusses scanning in a TFT: http://www.electronicsforu.com//EFYLinux/efyhome/cover/March...
"The TFT-LCD panel of the AMLCD is scanned sequentially line-by-line from top to bottom. Each line is selected by applying a pulse of +20V to gate line Gn, which turns on the TFTs in that specific row. Rows are deselected by applying –5V to G n-1 and G n+1, which turns off all the TFTs in the deselected rows and then the data signal is applied from the source driver to the pixel electrode. The voltage applied from the source driver, called ‘gray-scale voltage,’ decides the luminance of the pixel. The storage capacitor (CS) maintains the luminance of the pixel until the next frame signal voltage is applied. In this way, the next line is selected to turn on all the TFTs, then the data signal is fed from the source driver and hence scanning is done."
From my point of view you have not explained why it's not technologically feasible. You're merely describing that the current display tech isn't working that way.. of course not..
The motivation for the gridded layout is clear I think? You have this grid of transistors and you need to address them individually. Being able to drive an entire line and then select the columns is a good and relatively cheap solution. Now you can drive all pixels in one line concurrently if you need to and the performance of a single pixel becomes less of a bottleneck. So the row/col grid structure isn't a result of needing to be compatible with CRTs... Also naturally accessing in sequence allows you to simply send the data and clock down the line. Random access would require either multiplexing the coordinates or widening your bus.
I would imagine it's possible to design a random access LCD. You would need better performing individual pixels, you will almost certainly need more layers and more conductors, you will complicated your interfaces and protocols. So you end up with a more complex and expensive system for practically little benefit. In many applications (games, videos) all pixels change every frame.
Sub-scanning a rectangular portion of the display is maybe a more reasonable target.