I want to go back and address something
@Lanefan said earlier, to the effect that using player knowledge isn't fair to people who invest in those skills.
The corollary to my willingness to let players use whatever knowledge they have...or
think they have (mwuhahahahaha)...is that I treat proficiencies as having more potency than the mere numerical bonus the skills are supposed to confer. If somebody has proficiency in Arcana/Nature/Medicine/Whatever, I will tend to just default to automatic success when that skill is applicable. Which is
way better than just giving them an additional 10% or 15% on a roll. And this isn't (intentionally) to balance player knowledge, but because in both cases I would just rather that players have information and make decisions based on it, rather than gate challenges behind secrets.
So not only is there still value in knowledge skills, but I would argue there's even greater value to those skills than in games where DMs won't let players use their own knowledge, but do make them roll dice every time.