I have searched all over Apple's help and documentation I can't find any built in or app store apps that provide screen recording.
What prevents such an app to exist ? Are there any obvious technical reasons?
The technical reason no store app has screen recording is simply that no official API is provided from Apple to developers to perform screen recording.
The hardware is clearly capable of snapping still frames and storing / processing a video feed of the screen's size, so it's probably not a purely technical reason why it's currently not a feature of the OS.
Apple limits the degree to which iOS applications can communicate and "share". I'm not a developer, but I would be surprised if a screen recorder application is allowed under the rules or possible with the iOS APIs.
If this feature is important to you, send feedback to Apple explaining what you want and why it's important to you.