"Keep on" can be a beneficial feature some of the time (e.g. referring to a recipe), but other times it is a menace, and definitely should be an option, where the default is to power off normally, and a button could be added as a "hold open mode" in specific cases, upon request, and a user setting should be added to set up default behaviour.
This is an even bigger problem with Android because it combines with the "double tap to edit" feature which makes it too easy to accidentally open edit mode. (Wish we could turn THAT off, too, because there is a floating button already available anyway.) Due to both of these "features" I often run into the problem of leaving the phone on in my pocket (it does not auto off) and then butt-selecting (think butt-dialing) the text and replacing it with nonsense....UPDATE: while writing this I tested to see the double-tap to measure the time interval between taps and discovered it does not need a double-tap....just a single tap, wait 3 seconds, and you are in edit mode! WAY too easy to pop into edit note when reading or scrolling a note to read it! (I should start another thread on this...)