If nothing goes wrong during a repair, a backup isn't necessary. But a trouble free repair is not 100% guaranteed. There's a small chance that the phone could get bricked during a repair and apple knows this (and obviously has experienced it) so they make a point to scare people into backing up the device before sending it in - otherwise nobody would do it and they'd get the blame when things go wrong.
Removing the screen on a modern iPhone is a lot more risky than the old iPhones. The old iPhone screens were easy and relatively risk free to remove. The new phones have screens held in with gluey adhesive and getting them off is like performing open heart surgery on a patient (not my words but a direct quote from an apple repair tech).
He said- any time the screen is removed there's a risk of the phone getting irrecoverably damaged.