My concern with this - and I'm deliberately saying "concern with" and not "objection to", because like I mentioned earlier my thinking around these issues is tentative, not definitive - is that having the GM fill in the description is a bit like having the GM narrate who was the target of a PC's attack. Now there are some situations in which this is unobjectionable - eg an arena fight of PC vs a single opponent - but most of the time this is meant to be the player's job.Good question. I believe if you carefully read the description of the skill it should give you a general sense of the area that is searched with a single skill check. I remember seeing editions do this. But yes, failure to define this area is a part of the problem.
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this is a good place for the GM to help with the problem by responding "You scan the area around your feet carefully for traps, but see no evidence of anything immediately nearby." Indicating that he hasn't searched the whole hallway yet.
Here is what the Burning Wheel rulebook says about the "Assess" action (at p 151):
Assessing allows for a player [= character] to look for specific details - easy exits, the sources of that burning smell and unarmoured locations on the opponent . . . Such an assess nets the character a Perception test in search of what he described in his intent and task.
So a player can't just roll a Perception check and ask the GM to tell him/her everything that is interesting and worth noticing. This is one device for setting up the mechanics so that they mandate the player engaging with the fiction - in this case, choosing some specific detail that is worth looking for.