The conditions you give are certainly clear as day, but they're also "complicated and convoluted" to quote the spell description.
They cannot be both "clear" and "complicated/convoluted".
By your reasoning, a wizard could set the following condition: "Whenever someone calls my name three times, I'm teleported to his/her/its location."
Sure, why not? Of course, as DM I would note that the wizard failed to say "consecutively" and teleport him home as his servants are gossiping about him.
Contingency does have a drawback -- similar to Wish. You have to be careful in your condition, without getting too complex, or it will go off when you don't want it to. That limits the power of the spell, very simply.
If that's how I'm supposed to interpret contingency, I have a new house rule I guess.
Ah, so then we agree!
In all seriousness, you're welcome to rule it however you want in your own games. I'm merely providing an alternate interpretation; every DM will have to decide where on the spectrum they want their game to lie. Wizards are broken enough that allowing contingency to be something more than "blind, deaf, and dumb" isn't any more game breaking than 90% of their other abilities.
(an arrow, a fireball, a stone to flesh, a meteor swarm)
Tell me, how does the spell -- which only knows about the universe out to "one magical atom" away from the wizard's skin, remember -- distinguish between: an arrow and a dagger; a fireball and falling into the campfire; a meteor swarm and a handful of coals from a fire?
I still don't see how a contingency has any ability to act in response to stimuli that exist beyond its area. The spell description does not state that the contingency can react to such outside stimuli, and I don't see why it should be assumed that it does.
Because no explicit limits are stated. Nothing in the spell description limits the condition to things the wizard him/herself directly feels, experiences, or is aware of.
The examples in the PHB (falling into water for the instant water breathing and falling through the air for the feather fall or fly) are clear examples of how the spell works, involving stimuli that effect the contingency itself which surrounds only the caster.
The fact that these are the examples does not mean that they are the
only possible examples. If I told you dogs and cats had fur, would you assume that meant hamsters did not?
Water touches the contingency --> water breathing.
And it distinguishes from a heavy rain (or a bath) how?
Drastic drop in altitude and wind whipping by --> feather fall.
Gust of Wind? Jumping off a 10' wall on a windy day?
Examples are not enough to definitively state such limitations. I'm sorry, but they're not. You can houserule that way, but it is a houserule, plain and simple.
His contingency states that if he is ever successfully attacked from the back, a flesh to stone hits the attacker.
And yet, the spell can identify -- despite only being aware out to "one magical atom" from the wizard's body -- the attacker?
Not necessarily by the book
i.e. Houserule.
The contingency cannot save Azalin from the attack
Patently false. The condition states "is successfully attacked", not "takes damage", and the spell goes off as an Immediate Interrupt, which means the F-to-S takes effect before the attack is completed, nullifying it.
Why not just say, “If anyone tries to attack me from behind, a stoneskin is cast on me”?
Because it burns the contingency even if it's a L0 Commoner stabbing you with a spork. There's no point in wasting the contingency on a situation where you are not actually threatened.
The spell Elminster’s Evasion is another great example of how I interpret contingency spells. When any of the spell’s 6 conditions are met, Elminster is teleported to his personal safehold on a pocket plane. His personal trigger points for the spell are as follows:
1. His death.
2. The loss of his mental faculties (sleep, feeblemind, mind blast, insanity, etc.).
3. The loss of his physical faculties (paralyzation, petrification, polymorphed, amber sarcophagus, etc.).
4. The destruction of both upper limbs.
5. The destruction of his total body volume (disintegration).
6. His uttering the command word “Thaele.”
None of these conditions have anything to do with the world beyond the contingency surrounding Elminster.
You could just as easily argue that their generality is due to a smart caster, not such requirements. Stating "loss of mental faculties" protects against a whole wealth of conditions, as you note (sleep, feeblemind, etc), while stating "any time anyone casts feeblemind at me" only protects against that single spell, and not Touch of Idiocy, etc.
To go back to my first paragraph, Elminster does, in fact, hear his name spoken by anyone who utters it anywhere on Faerun, but that’s a power granted by Mystra herself, and even then Elminster would have to scry/teleport in the following rounds. How a 6th level contingency could duplicate that is beyond me.
Because a 6th level contingency can only have 1 active at a time and is discharged when the conditions are met. Elminster's capabilities have more than 1 active at a time and are not discharged when the conditions are met, thus meriting higher than a 6th-level spell, for obvious reasons.