Well search is all about deducing, whereas spot is just perception (notice something in your peripheral that you judge to be out of the ordinary).
That's the reason. Otherwise, if you were using wis to search then you'd be judging where an object could be based on what makes sense to you and most likely might end up biased to the point that you can't find the object because reality contradicts bias (hence, deduction is required).
In layman's terms, using wis is like asking 'why would this object not be here? Well theoretically it should be located somewhere else because that's the only other place I would store the object and no one I know of cares about the object besides me and I've never had a history of people stealing my things so if it's not in that location, then finding it is hopeless' - all about induction and forethought.
Int would be 'if the object is not here then the probability of it being in another location is increased, hence I should keep looking'.