When 'Enable Restrictions' feature is turned on, you might not be able to download an app.
This issue might occur if incorrect Apple ID is used in the App Store. Apple ID issues: the apps in your iPhone will get downloaded only if you are signed in with your own Apple ID.
If you are searching answers for 'why won't my iPhone let me download apps', just check the possible reasons for it now. Why Won't My iPhone Let Me Download Apps?