Frequency of search varies widely across apps. In a browser or address book, it's fairly frequent throughout your use of the app. In a calendar or music app, it's a bit less important. In a weather app, it's probably infrequent (unless you're a globetrotter or similar). In a notes app, it's something you'll usually use when you've just started using the app after minutes/hours/days of not using it. And so on.
So we shouldn't necessarily expect a search feature (or a share feature, or a print feature...) to be accessed in exactly the same way in every app. Consistent position can be good for learnability, but it also risks making a feature invisible. (The same is true on the PC: "Find" might always be in the "Edit" menu, but outside of menus, the prominence of a search command varies widely between apps, as it should.)
The case of System Settings is similar to a notes app: search is something you're most likely to use when you're entering the app after some time not using it. Specifically, when you've decided to change a setting and you're looking for that setting. So I think it's correct for the search to be visible by default on the main screen, not even requiring a tap to get to; for it to scroll out of the way if you move down to the categories; and for it not to be present at all on secondary screens. And the first two of these mean that it can't be in the header.
Thanks for the suggestion.
Frequency of search varies widely across apps. In a browser or address book, it's fairly frequent throughout your use of the app. In a calendar or music app, it's a bit less important. In a weather app, it's probably infrequent (unless you're a globetrotter or similar). In a notes app, it's something you'll usually use when you've just started using the app after minutes/hours/days of not using it. And so on.
So we shouldn't necessarily expect a search feature (or a share feature, or a print feature...) to be accessed in exactly the same way in every app. Consistent position can be good for learnability, but it also risks making a feature invisible. (The same is true on the PC: "Find" might always be in the "Edit" menu, but outside of menus, the prominence of a search command varies widely between apps, as it should.)
The case of System Settings is similar to a notes app: search is something you're most likely to use when you're entering the app after some time not using it. Specifically, when you've decided to change a setting and you're looking for that setting. So I think it's correct for the search to be visible by default on the main screen, not even requiring a tap to get to; for it to scroll out of the way if you move down to the categories; and for it not to be present at all on secondary screens. And the first two of these mean that it can't be in the header.