Perhaps forced rarity is a better term?
It's a bad concept.
Be Mine was forced rarity. Regardless of effort or capability, some people could not get it.
Maybe it's just me, but one of the nice things about WoW is that in an artificial world, we have control. In WoW it's a lot easier to have an internal locus of control, to believe that our actions are what matter, rather than some overall forces. Sure the devs matter: they matter for their creation of this world in which we decide our fates. We decide how far we will get in raiding. WoW can create an ideal world in the sense that we are truly free to pursue what we desire and there is no racism to hold back some people, lack of educational opportunities to hold back others, or rich parents to boost ahead a small few. We all play the same selection of 10 classes, with the same spells, with an AH which does not discriminate. Sure time is an issue, but ultimately personal determination is more important than most external factors.
In other words, WoW is great because it creates a world where you choose what you want to accomplish.
Forced rarity breaks this. Be Mine was a good example (good example of a bad thing). Random drops are this as well. I remember some silly news program where they claimed someone was great because they had Ashes of Alar. Oh sure, killing Kael'thas wasn't nothing, but the mount? That was luck. There were a thousand times as many people who killed him and received no mount.
The upcoming change to the Glory of the X achievements also breaks this. According to Bornakk they're removing the drakes. Why? They think Ulduar gear will trivialize them and they want them to be rare. Fine. But this is the wrong approach. This change only means that if you started WotLK late, too bad. If you leveled slowly, too bad. Maybe you were slow to get into raiding, too bad. This is wrong. It's forced rarity.
What's a better method? Maintain the difficulty past Ulduar. Add an iLevel maximum for the achievements and leave the mounts. This way you cannot trivialize them with gear because you can't get past a certain gear level. All Ulduar can give you is more experience with your class rather than a way to bypass the challenge.
The mounts will remain rare based on their difficulty.
Though I'm tempted to go for the other direction. Let them be trivialized. Let every noob and scrub get one, for free, for nothing, after 3.1. Then go back to the people that burned through content and will then bitch about it and just laugh. laugh and laugh at them. Explain that they are harmful to WoW. Their elitism, their desire to burn through content and then bitch when it runs out, that is harmful. Blizzard probably couldn't get away with canceling their accounts, but annoying them, hurting their egos, that might get the job done the same way.
Random is stupid.
Time-dependent is almost as stupid.
Anything based on either of these should be a feat of strength.