Does this type of memory-mapping for a display exist?
In your 31 bit solution, the thing most likely to happen there is that you'd give an extra bit to green and make a 32 bit solution.  In 16 bit color for instance, r and b get 5 bits while g gets 6 bits, because your eye can distinguish more greens.

Or maybe you'd use that extra bit to have 1 bit alpha? Not sure if that'd be very useful though...

As far as the rest, whether you have a gpu or not, writing to single pixels at a time is bad form.

Instead, you ideally want to do block operations that either fill or copy large strips of memory.

For some things, like alpha blending, that isn't able to be done as a block operation very easily so is a more expensive operation in general.

As a solution to this, modern computers have a processor that is closer to the video memory, so there isn't too much latency when pushing pixels back and forth across the main bus to do things like calculate alpha blended values involving the source and destination pixel.

Also, instead of fewer more powerful cores, there are many less powerful cores, which helps address the situation of needing "one off" pixel operations.

That processor I'm referring to is the gpu and the programs you write for it are called shaders (;

What you are asking about doesn't exist to my knowledge and seems like a bad usage pattern, so seems unlikely to exist IMO.