A card cares whether it has the Mental trait primarily in a check, when immunity is clearly defined. It would require new rules to say "While examining cards, if a card is immune to a particular trait, it cannot be found in the examination process," and those rules would not improve the game experience. So no Mental trait for Detect Thoughts, even though the flavor seems like it might have it.
To be fair, there's a very large number of cards with the Mental trait that in no way interact with immunities or checks. For example, Mind Probe from the Occult Adventures 1 Character Deck (and, in fact, quite a lot of Mental-traited cards in the Occult Adventures decks). I would argue the trait still adds to the game experience; it's quite relevant, and has been even as far back as the original Rise of the Runelords where there have been powers which interact with the Mental trait, such as "Automatically recharge spells with the mental trait", etc.
With that said, Detect Thoughts has never had the Mental trait, it's been printed multiple times and reprints never change the traits on a card. Thematic or not, it seems largely too late, from my perspective.