Here is the YouTube link: https://www.youtube.com/watch?v=J-3c1NYF8GwThe iphone 5s home button CAN be scratched. If you look on youtube you will see someone doing so to demonstrate the consequences of a scratched touch sensor. The end result is that the touch id no longer works to access your phone!
It's not all that strange. Temperature plays a significant part in this. I assume it's getting warmer where you are?Mine was shaky at first, but over time it seems to have gotten better. Kind of strange.
Why don't you go to 'Settings" and create a touch Home button that displays on your screen. You can turn off from there too.My iPhone 5 home button has scratches, which is to be expected from plastic. Is the 5S home button, which is partly sapphire, resistant to scratches? How durable is the capacitive ring?