If a home computer or console has two banks of memory, A and B, then the following design is possible:
The video chip only connects to bank A. The CPU connects to both. During active scan line, CPU access to bank A is slow because it must share bandwidth with the video chip, but it can access bank B at full speed. This is useful because you can put code and non-video data in bank B, though the CPU will still hit some slowdown because it must write to bank A in order to prepare the next frame while the current one is showing.
The Amiga is perhaps the best-known example of this design; the two banks were called chip memory (the first 512K) and fast memory (the rest), respectively. The 48K Spectrum was also a popular example; the two banks were the first 16K and the other 32K respectively.
It seems to me you could improve performance with a variant design: as above, except the video chip and the CPU each connect to both banks.
In the first frame, the video chip displays from bank A while the CPU prepares the next frame in bank B.
In the second frame, the video chip switches to displaying from bank B while the CPU prepares the next frame in bank A.
In the third frame, it switches back to the first arrangement, etc.
It seems to me this fairly minor variation on the historical design would allow the CPU to always work at full speed even when writing the data for the next frame. (In this context, I'm just thinking about scenarios where the CPU does that work, not ones where the video chip itself contains acceleration hardware that writes to video memory.)
Did any historical machines work the way I suggest, with video chip and CPU switching back-and-forth between two banks each frame? If not, why not? Is there some disadvantage I'm not taking into account?