ahhh, I think there's the source of our confusion: I suspect you are actually talking about NOR flash?
NOR flash is physically organized different from NAND. It typically does allow single word/byte or sometimes even bit level accesses, like you described. NOR flash is also much more reliable, often not needing any wear leveling at all. The downside is that NOR flash has orders of magnitudes lower data density.
Microcontrollers would use NOR flash internally for program memory, precisely because it allows direct, single-cycle access to individual opcodes. With NAND flash, program memory would have to be read page-wise and require some sort of instruction cache in between. Other EEPROM-like devices (e.g. AT28Fxxx) also use NOR flash for pretty much the same reasons.
On some embedded Linux devices, NOR flash is used for config/boot loader/kernel, while the rootfs lives on NAND.