It's hard to speak about feasibility in absolute terms here. I would disagree that the current tech is the way it is simply because of the history of CRTs (though there's definitely some influence). Displays have evolved to their current technology by optimizing for things like manufacturability, price and performance. Those obviously would come ahead of CRT compatiblity.

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.