Some things, admittedly, are not necessarily well-modeled in the rules. That makes it harder to see the implications.
OAs/AoOs are based on a real life thing- the ability to see movement and react. Humans are very, very good at picking out movement, even stealthy, slow movement. Handy for noticing predators. Teleporting likely wouldn't trigger the same kind of reaction.
It has been said, for instance, that a fit man can charge @25' in the time it takes most humans (not quick-draw specialists) to draw and aim a gun. In that time, the intended victim notices the movement, assesses the intent to harm, and begins the process of arming himself. The 30' teleport- being instantaneous- both increases that distance AND removes the initial visual stimulus: your attacker doesn't move towards you, he is simply there. He doesn't alert you by stepping on a twig or accidentally trigger that tripwire you set up, either.
If you're a bodyguard or sentry, this is bad news.
Imagine having to cross a guarded greathall to continue on your mission. It's possible that you might assess the risk of attempting to cross is to great, and you might seek a different path; your mission might even be thwarted completely.
An eladrin might simply be able to 'port across without a problem.
The whole curtain thing? A conventional sneak would have to open the curtain and physically move beyond it, a potentially very obvious thing. The eladrin needs only to pull it back a centimeter or so.
Vs pike formation isn't a problem. Pike formations depend on several rows of pikemen holding a 2-handed weapon out, so that anyone attempting to get in among them faces lots of spear points. Each row protects the man in front of him. Very hard for an attacker to avoid getting poked. But a single armed eladrin could simply teleport to the interior of the formation, in among people with their hands full. As soon as they start to drop pikes to deal with the killer in their midst, the periphery of the formation is instantly diminished in strength. If he can't fight his way out, he's toast and the square reforms...until the next one blinks in. And if they popped in in teams or waves, the formation would fail quickly.
Shield walls face the same problem.
How many targets could a trained archery formation drop in 30' before they have to either prepare for HTH combat or break & run? What happens when that last 30' can be covered in the blink of an eye?