What you are describing is parallel access memory. Most memory was like that back years ago. When memory was small, bringing out all the address and data lines separately was at least feasible. A common static RAM back in the 1970s was 1 kBits organized as individual bits. It therefore had 10 address lines, one data line, and a few lines that caused reading and writing to happen.
Today, such a memory would be absurd due to the large number of pins it would require. For high speed systems, memories are still parallel access, but the pins are usually multiplexed. For example, there may only be half the number of address pins as address bits, and it takes two cycles to read in a arbitrary address. Most accesses are sequential, and the controllers are smart enough to only write the upper bits when they need to be changed.
Micocontrollers don't need the speed of large systems with large memories, but their pins are limited, so serial makes more sense. Of course now significant memory is built into microcontrollers, which is even simpler to access than a external chip.