The literal only game I've ever seen weapon durability be used in a fun way is Riviera the Promised Land.

Characters don't traditionally level up, they "Skill Up" by filling the EXP Gauge of weapons they've acquired, increasing their stats based on the weapon used and each character gaining unique Over Skills(super attacks that drain a lot more of the weapon's durability) that can be applied to every copy of every weapon you receive. The MC has an unbreakable weapon that gets better as the game goes along, but if you aren't using random chaff items in the field, you aren't getting those precious Skill Ups that you'll want for stats, and you'll also be losing out on potentially viable Over Skills that have different targeting, power levels, and special attributes that the main weapon doesn't have, which encourages you to regularly just chew through your junk gear rather than stick to just one. There's also a few extremely powerful weapons that you'll be generally not likely to use in standard fights because of how rare they are and the fact that all of them can still break, but if you S-Rank a battle(yes there's a ranking system in this turn-based JRPG), you get more Trigger Points where you can activate things like treasure chests or alternate pathways in the game's Questing Mode, which frequently give you more enemy encounters and more items. Sometimes it's better to use that rare sword's limited uses to one-shot a durable enemy than it is to use your cheap garbage sword to preserve the rare one, because you'll potentially get a rare spear as a reward for S-Ranking and open a treasure chest that also has a rare bow in it.