Repairing other peoples gear in a dungeon is an awful idea. The ways SE could implement it,either:
1) you'd spend your own gil to repair a strangers gear because they're a sandbag. If the event you have to do this for 7 people in your party... RIP your own personal stock for self repairs. Followed by forum threads titled "I repaired 7 peoples gear in Shinryu Ex and then they vote kicked me"
2) they'd have to remember to carry their own stock of carbon matters, and they already can't even remember to repair at a vendor. Followed by forum threads titles "SE we need more inventory space because we have to carry materials for repairs"
3) Put a repair NPC at the start of every dungeon. Lore wise, this makes 0 sense. Probably a better option still compared to #1 and #2.

What would absolutely not work and never be on the table as a possible discussion?
Preventing queue based on durability. DPS especially can have some lengthy wait times. Even if they Q up at 41% durability, a few deaths while fate grinding might have them drop below a safe threshold just as their duty finally pops. There's no all inclusive solution for requiring a durability value for a duty.

Possible solution 4) Just negate durability loss in duties. Fixes all issues. Followed by forum threads titled "SE just go the extra step and remove all durability and repair functions from the game, because the entire concept has completely failed as a gil sink since patch 2.1 when you added gil to dungeon mobs SPECIFICALLY to cover repair costs, and it adds less depth to the game than it adds headaches with all this personal responsibility to repair, followed by dev time wasted trying to develop ways to remind people to be responsible in regards to their gear when grouping with others."