Except that Stealth Rock is a specific field effect, whereas evasion is a stat. I don't care if you increase +2 defense from Iron Defense or Acid Armor, it's the same net effect and the game doesn't care how you do it. Likewise, if there was some move not called Stealth Rock that had the side effect of causing the field effect Stealth Rock (for example, if Rock Smash had a 20% chance of laying rocks on the opponent's field or something), then this would still prevent against that, too. Field effects are different than specific moves, so your Double Team comparison doesn't make any sense.
I agree that my Double Team comparison is not completely equivalent. But it's closer than you say. I think the general field effect is the same as Spikes and other moves that cause passive damage. In your example, you mention Iron Defense and Acid Armor. Same net effect, different move types. In the case of Stealth Rock and Spikes, it's pretty much the same thing. One is Ground, the other is Rock. Yes, Spikes can be layered, but the field effect is pretty much the same. That's why Rapid Spin clears all of them. To have an ability that singles out one specific move that causes that field effect is inconsistent with the game. You can target the move type, or the move effect. But, to target both specifically? I don't think so.
My general point is that, in Stealth Rock, the pokemon metagame has identified a single move that is particularly disruptive. Is it disruptive to the general game of Pokemon? Not really. I suspect that Ninty thought it was roughly on the same level as Toxic Spikes. To the metagame, it's far more impactful. Yes, Toxic Spikes added a new dimension to passive damage. But, nothing like Stealth Rock. Stealth Rock took almost all Flying, Fire, and Bug pokemon and made them worthless in the metagame. Did Ninty intend that? Probably not. Do they care? Probably not. I don't really know. I'm just guessing.
Does Nintendo care that Ice Shard impacted the metagame more than Bullet Punch? No. I think they came up with a few more priority moves and made one Steel and one Ice. It just so happens that the ice version makes a hella difference in curbing ScarfChomps and all sorts of other metagame horrors. But, if we came up with an ability that affected priority moves, it should affect all of them. We couldn't just single out Ice Shard because it matters to the metagame, or Mach Punch because it doesn't affect Ghosts.
I think Ice Shell and Mountaineer are both "well-formed" abilities. One affects all indirect damage, the other affects all Rock damage. That makes sense, in general Pokemon terms. As for the metagame, we shouldn't focus solely on that.