So, what makes it not a general purpose computing platform? Unless you mean to argue that a computer with a Xen 2 CPU, RDNA 2 GPU, running an OS based off of Windows 11 that can run Universal Windows applications is not general-purpose.
Public perception. An overwhelming majority of people who buy an Xbox (or a PlayStation, or a Switch) buy one just to play games. They don't expect it to do anything else. The manufacturers don't market their consoles as general-purpose devices either, they market them specifically as appliances for playing video games. Their SDKs also aren't publicly available.
If building iOS apps in 2008 was the same process as console games, would the iPhone be as successful as it is today? Imagine having to be a company, proving that your app idea is worthwhile, signing a million NDAs, and finally getting a devkit just so you could make a farting app (those were popular in the early days of the app store). The app review process back then was also much more forgiving and sensible than it is today. Things Apple does when it has to compete on its own merits!