Do we know *for sure* that this is a hardware problem? And if so, what the nature of it is (aside from the 'fix' is twist your phone)? e.g. Is it caused by a loose connector, does it appear after a phone is dropped, overheated, submerged, etc?
I've seem similar (though not exact) problems on older phone models when upgrading to later versions of iOS. I keep wondering in the back of my mind if some event loop is missing certain hardware events because something else is off doing processing in a foreground thread that it shouldn't be.
Anyhow -- I ran into this situation and was able to cause the problem to repeat on demand.
A friend had emailed me a message that had short sentence that was telling me he was doing something tomorrow. The sentence split between two lines, and Apple's calendaring parser identified the word 'tomorrow' at the end of the sentence and made it a clickable link to try to make an event from context.
I, however, wanted to select the sentence to perform a reply. Trying to select the word in a forward direction kept popping up the Calendar create-event dialog, to which I hit cancel. Did this two or three times. [Remember Apple's calendar features have always been a little wonky.]
So then I tried selecting the sentence backwards, starting at the period, and dragging upward through the link to the next line. What was weird was that it was selecting all but the first letter of the sentence. When the cut/paste/select-all popup appeared, I started to select select all (it was in a pushed state), and then I thought better of it and continued to drag upward out of the popup to deselect it. The moment I did, the menu went away, and the screen became non-responsive to touch and scroll events.
I waited about 10 seconds to see if there was some internal event queue that needed clearing out. Nope. Phone seemed dead. I tapped the power button turning off the screen and back on. And I was right back in the same email at the same spot on the screen -- touch restored.
So, I selected some sentences, forward and backwards, moving the selection pins. No problem selecting words.
Hypothesizing the selection over a generated iCal link might be causing some one-off problem, I did the same procedure. Drag from the end of the sentence, through the link, to the start of the sentence, and again, it didn't select the first letter of the sentence. Dragged through Select All then off it again, and REPEATABILITY -- the screen froze in the exact same way.
This is where I screwed the pooch -- I should of had a camera rolling, or at least done it a third time in front of a camera. Because my next thought was to reboot the phone (back to the Apple logo) and try first thing, absolutely fresh. However, this time the selection worked.
Since this point, I've found that my iPhone 6 Plus tends to exhibit the problem more often after a number of cut'n'paste occurrences, but haven't been able to nail down something as repeatable.
Hopefully this can help someone here create a use case for proof for Apple.