I’ve got a similar problem with the Pi Touch 2 screen. Your solution also works. However, I found that the Pi Touch 2 screen works fine in portrait mode (which is what it defaults to). The touch device is listed as “floating” but seems to work. When I rotate the screen, the touch screen doesn’t respond unless I do the xinput enable 6 line.
Incidentally, there is another person with a Touch 2 with similar problems to me:
His solution is to rerun udev rules - which also seems to have the same effect as the xinput enable 6.
Have you made any progress?