Most modern CPUs can do exactly what you are stating, as they have the graphical processing capability right on the chip itself. This is enough for most office or school computers, as well as low powered laptops. Generally, GPUs are needed for more difficult tasks that are beyond the capabilities of what a CPU can handle. For example, a very detailed game or computer graphical design will almost require a separate GPU in the PC. However, there are some CPU models that lack the "graphics chips" or are there but disabled by the manufacturer, generally a cheaper model of a CPU.

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With that being said, if someone was building a budget PC, with very light gaming, you can just get a modern CPU capable of onboard graphics for low end performance.

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Although I feel like your question may be as to why a CPU itself would need *any form* of a graphics unit, even if it is "on the chip" as with many modern CPUs. The CPU, strictly speaking, does computations in and of itself, at a very fast rate. However, it does not have the ability to do the output frequency conversions needed for standards that make the PC capable of connecting to an HDMI, VGA, Displayport etc. It is the same notion that necessitates having system ram, a hard disk, and other peripherals attached to do what you want to do.