In sending the entire frame with every refresh you get pixel addressing "for free", since you just send the data for each pixel sequentially in a predefined order. If you only wanted to update a single pixel, you would need to effectively send an instruction saying "set pixel x to rgb: a, b, c" or whatever, including both the pixel colour values and the pixel address. You'd also need some sort of edge detection for when a pixel is supposed to change which adds a delay.
This is fine for one pixel, but if every pixel on the screen changes at once then suddenly you are going to be sending a hell of a lot of instructions that not only contain the colour values as in the "old crt style" method, but also the address of every individual pixel too, which will then have to be decoded by the screen-side hardware.
All in all, you'll be using a lot more bandwidth and will need a much faster clock to do all of that in the same period of time. In the old school way, you just have a pixel clock that matches the pixel rate and some serdes for serialisation/deserialisation on each end which imo is considerably simpler.