My original conception for "Wear and Tear" is different than what ended up getting released. This is pretty common for the mod (and for games in general), as we iterated over the design.
My original design for the W&T mechanic was that it was a fixed chance (independent of HP loss), but that the item would be DESTROYED, not damaged. This would have been combined with a reduction in the up-front cost.
However, this intersected with another new feature going into beta 15, which was the re-introduction of the (vanilla) mechanic for repairing MEC suits. In vanilla, this only happened if the MEC was killed, which was a bit to much of a boundary condition, so it was extended to cover being wounded (which is all the info that the tactical game passes back to the strategy). Having added the mechanic for MEC suits, it seemed odd to be singling only those items out, and not other soldier gear, so it was extended to cover soldier gear in general.
From my perspective, the item repair mechanic is intended to address 2 issues.
1) Item vs soldier utility
From articles I've read (interviews with Ananda Gupta), vanilla XCOM:EU (pre-release) suffered from a problem in that the items felt more important than the soldiers. This was before the perk trees were added -- most perks were attached to weapons (e.g. squadsight to sniper rifle), so the utility was attached to the weapons instead of to the soldiers. The perk trees were added in order to correct this.
In Long War it had become clear we'd tilted this back toward items being overly important, since we'd added a fatigue mechanic for soldiers, but none for items. Essentially you can view the item damage/repair system as the equivalent of soldier fatigue, but for soldiers.
2) Falling off a cliff when losing items
Because items were almost never lost/damaged and could be shared around the barracks, item costs had to go up in order to balance this. This in turn lead to a pretty massive penalty when items were lost as a result of soldiers being killed, resulting in a double whammy. Feedback was that the item loss was perceived as more damaging to the campaign than soldier loss.
The way around this was to reduce item costs, but some other mechanic had to be introduced to help balance out the overall game -- and that mechanic was item repair.