Your whole framing here seems to rest on an unarticulated assumption that makes no sense to me. The assumption you're making is something along the following lines: that resolution is independent of the significance, to the characters, of what is taking place in the fiction. That assumption is false, as far as Burning Wheel is concerned.Right. So who opens the safe will affect the contents of the safe. But the characters presumably don't think this is the case, yet the players know it to be so. This sort of system causes almost complete disconnect between the decision making process of the players and the decision making process of the characters. Hell, why would the characters even debate who opens the safe? They certainly cannot know it would in any way or form affect the contents! In universe it would make perfect sense for one character to say "Go ahead, you do it, you're good with locks. But I sure hope it's those papers in there rather than just some pointless gold you're always after!"
This obviously doesn't bug you, and good for you. But it would bug me massively.
You're positing two PCs. You've said nothing about what their relationship is. Nor their Beliefs. You're now positing that one is opening the safe at the request of the other. How does that relate to the two characters? Did the second PC acquiesce in the request? Were they persuaded? Threatened? Do they have a Belief about helping their friend? Or thwarting their frenemy? Or something else? And what intent has their player stated, in relation to their action of opening the safe?
The last time I had a BW PC search a place, it was Evard's tower.
Aramina had the Belief I'm not going to finish my career with no spellbooks and an empty purse!. Thurgon and Aramina, travelling along the Jewel River, debated what their destination should be. Aramina, being learned in Great Masters-wise, believes that the abandoned tower of Evard the Black lay somewhere in the forest on the north side of the river, and wanted to check it out. Mechanically, I succeeded in a Great Masters-wise test for Aramina.
After some time, Thurgon acceded to Aramina's desire that they investigate the tower. Thurgon's Beliefs included I am a Knight of the Iron Tower: by devotion and example I will lead the righteous to glorious victory and Harm and infamy will befall Auxol no more! (Auxol being his family estate; Thurgon has a Relationship with his mother, and an Affiliation with his family). The characters met Friedrich, a former knight of Thurgon's order who poles his skiff along the river (successful Circles test for Thurgon), and he took them to the tower. A demon was also there (maybe waiting for them? - this was the GM's decision about framing) and Thurgon fought it to a standstill. When Thurgon entered the tower and searched it, a Scavenging check failed. Thurgon found things he didn't want to find - old letters that suggested his mother was Evard's daughter. Aramina had swooned while fighting the demon (due to the tax of attempting to cast a spell) and so didn't know about the letters, which Thurgon subsequently burned. She found spellbooks in the tower, but as best I recall the GM didn't even ask for a test to find those: all the action had already been resolved (finding the tower, the demon, the letters).
That sort of interweaving of the PCs' Beliefs and Relationships is key to GMing Burning Wheel. The GM's principal job is to apply pressure on them. A player's principal job is to pursue them: as p 269 of Revised puts it, players "must use their characters to drive the story forward - to resolve conflicts and create new ones. Players are supposed to push and risk their characters, so they grow and change in unforeseen ways." In the case of the safe, each character has a reason for being there, be that finding the dirt, honouring a promise, helping a friend, or maybe betraying one. Those are the considerations that will inform players' declarations of intent, and that the GM will have in mind in narrating consequences.
It is not just colour, it affects the odds massively. In fact GMs determination of the difficulty affects things way more steeply in BW than in 5e D&D, and it is far easier to make things virtually or literally impossible. Why on Earth would such a huge impact be given to simulationist measures such as safe quality, which has basically nothing to do with what you're actually intertest about, that being the beliefs and desires of the characters?
All I can do is repeat that they are not simulationist concerns. The reason for using "objective" DCs is not to explore the fiction for its own sake. It is to establish the colour of the setting and situation. The Adventure Burner explains this (p 264):Right, good point. I was really thinking mostly about BW where the difficulty drawn from simulationist considerations has a huge impact.
[T]hese obstacles create setting. When a player acts in the game, he needs a difficulty for his test. The obstacle is the number; but it's also the object of adversity in the fiction. Obstacles, over time, create a sense of space and logic in the game world. When a player repeatedly meets the same obstacle for the same task, he knows what to expect and he knows how to set up his character to best overcome this problem, or he knows enough to find another way around.
Some things are harder than others. And this colour then generates decision-making in the resolution system - FoRKing other skills, getting help, using gear, spending Fate and Persona, spending time practising to get better, etc. That's part of the point of the system.