For those missions in which you face a variety of enemies e.g. slimes in one room and skeletons in another: Complete the mission without changing anyone's gear.
It makes sense but I think it would probably be way too easy to warrant that rare loot. All battles in one adventure are quite similar. If you build a deck that is great in the first battle, there's a high probability that it's great in others as well. And if not great, at least sufficient to finish the adventure. There are only a few adventures where enemies chance so dramatically that tweaking is required. I'm pretty sure that the only adventure where I've ever changed my party mid-adventure was Lord Batford's Manor because Missile Block is useful in that throne room with all those archers. But even that was the drawback challenge - I did the regular adventure without Missile Block. If new quests were added, I'd rather see something that required a different approach to deckbuilding, like having to use nothing but common cards etc. So it's not a bad idea but I personally think it would be too easy. If adventures were more diverse, it would make lot more sense.
Setting them only for those adventures where not changing builds would be difficult - rather than for all adventures would solve that issue. I believe the quests are set manually, so this could still work. The common deck idea is also great, but could work on most quests - as a more sweeping inclusion.
I think no gear-change would probably be best combined with no deaths. Certainly there are only a minority of missions where it would work. I agree that the 'common cards only' idea is very good. And the people who feel they never get rare drops should like them, as in theory they should find these quests easier having got more common cards!
