Re: OK, so can run a game server on a switch
It's cheaper.. The likes of Arm, Qualcomm etc are designing and building relatively powerful processors for use in consumer devices, such as Phones. Because they are turning them out by the million, the price per unit is incredibly low.
Now, Cisco comes along. They want to build a new switch. They are looking for a CPU. What do they go for? Custom designed silicon, that has enough processing power for their needs, but comes with a design cost as well as a manufacturing cost? Or an existing CPU that they can either use without change, or base a new CPU on? Bearing in mind that designing a new CPU can cost millions, even before you've produced your first chip.
Another reason is processing headroom. With more and more services being added to network hardware (such as local caches in a content distribution network), more processing power will be needed, but companies aren't go to rip out all their networking hardware regularly, especially bearing in mind some companies will have thousands of items of networking hardware. In short, with networking hardware, because you aren't going to replace it regularly, you work out how much processing power, storage and bandwidth you actually need, then at least double it.