What it really comes down to is "what YOUR game requires" and not "Does it belong in D&D at all".
Consider this:
In 1st Ed OD&D, the only class that could detect and disarm traps was the Thief (and it was only a 10% chance). At first glance, this did not seem fair. "My fighter has just as much a chance to see a tripwire as he does. Why can't I search for traps?"
Here's your reasoning:
Your standard fighter does not typically deal with traps. Maybe, once upon a time, a Thief friend showed him a few traps and how they work... and maybe he made an attempt to remember. But his lifestyle does not put it at the forefront of his mind.
Eventually, he walks into a corridor, remembers there's traps, looks for tripwires and plates for a few seconds and thinks all is good. His hand goes to his hilt awaiting ambush and presses-on. What he did not consider is the stream of air holding a metal leaf at bay. He interrupted the air and the metal leaf trips the rest of the trap.
- A Bard views the world as a stage and has his inner dialogue narrating his story in his head.
- A Ranger views the world as though he is the center dot in a target. He keeps his eyes on the tree lines watching for other center dots.
- A Wizard views the world around him through an imagined lens watching for magic. If it's mundane, it's exactly that. If it's magic, then, "Stand back and let me handle this. I'm educated and you're not."
- An Acrobat views the world as foothold, fingerhold, or hazard. "Anything but the ground like the rest of the world. I belong up there."
- ... and the thief? -- "Everything is out to get me. If I owned that book - If I needed that door shut - If I wanted an intruder dead - what would I do to make sure that happened?"
Where other classes are just as aware of traps and hazards as the thief is of ambush and magic, his bread and butter is intrusion.
How do YOU view the world?
You KNOW icy roads are dangerous. But often you think, "If I'm careful..." Then you find that your car starts spinning and there was nothing you could do about it, and our fellow gamer friend in the passenger seat says, "Fumbled your driving check"... When in fact, you are not a professional driver - but you know how to drive.
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But what of wizards and magical traps?
Wizards traps are less "traps" and more "wards". Some may say they are the same, and I say, "you're right", but let's put definitions aside and view them more as intentions.
A trap is set to keep intruders from a physical structure or item. Often this is because they are set by mundane people to protect mundane items.
A ward is a spell set with the intent of protecting a wizard's belongings (often spellbooks and magic items).
In some cases, a Wizard may be under the employment of a mundane person to protect mundane things: important information, evil castles, etc. In which case a GM would rule one of three ways:
- A Thief would not know of magical traps and trip it.
- A Thief would notice a magical trap but accept that it is beyond his means of disarmament.
- A Thief would be quite familiar with magical traps and mundane means to disarm or avoid it.
For this reason, the party should be balanced. Magic and Thievery should work hand-in-hand... at least it was the original intention.
But then came the time when players forgot about the "spirit of the game" and it became a game of "us vs. the GM". Players started looking at the rules as obstacles to be overcome or circumvented, rather than a means to interact with the D&D realm. Defiance was mistaken for cleverness... and in some cases rewarded with XP. Good times and high-fives for odd ways to overcome, were soon replaced with common place expected results. From then-on it was how the game was SUPPOSED to be played.
So cross-class skills were introduced where ANYONE can learn a skill their class typically wouldn't know, "because I want a guy that knows how to do it... call it a hobby of his outside of his profession".
... but it was too late, and the spirit of the game was dead. In the spirit of Magic: The Gathering, it's all about finding loopholes in the rules in order to find the solution to the puzzle or trap in the game.
So in the end, it's all about what kind of game you are running. Personally, I think EVERYONE should spend a weekend or two playing OD&D to remember what it was like and why we played.