We already do. In modern systems our CPU is only tasked with directly handling memory and the GPU. Handling of basic I/O is the chipset's responsibility. Obviously the CPU still has to be involved on some level or another as it's the primary decision maker, but the mundane stuff is all handled by the chipset or some other chip that's soldered to the motherboard.
The advantage of having a chipset is that we get more flexibility as to what I/O we want to include on a motherboard. For example if you don't need as many USB or SATA ports on your motherboard a cheaper chipset could be a better solution.
The disadvantages are an increase in motherboard cost/complexity and an increase in latency. The increase in latency is why the CPU directly handles the memory and GPU. While less latency sensitive tasks (like network or USB ports, etc.) are handled by the chipset or another onboard chip.
SOCs (System on a Chip) are typically only used where performance and I/O flexibility are secondary considerations and things like cost, power consumption and reduced complexity is preferred. Like in your cell phone for example.
