To answer the leading questions, let's take them one at a time:
Jhaelen said:
Well, at least twice: the first time you're surprised by its ability, the second time you expect it and act accordingly.
I immediately see two questions here:
1) Is the old bugbear which doesn't have a cool move better in that regard? How many times can you fight a 3E standard bugbear before it gets old?
There are two points to make here. First the monster with no tricks doesn't get old as quickly as the one trick pony. Why is that? Because the monster with no tricks operates in an ordinary field. Something that is supposed to be ordinary does not suffer because general strategies and tactics suffice against it. That is the meat and potatoes of the game. After eight years of playing 3.x, I still enjoy pitting my players or my characters against orcs.
On the other hand, things that are supposed to be extraordinary get old much more quickly. Even though my characters have probably fought fewer half-dragons and half-fiends together than they have seen orcs in a single battle, I'm sick and tired of half-dragons and half-fiends.
The ordinary does not suffer for being common. It's supposed to be that way. Likewise, lustre of the unique trick often wears off as soon as it ceases to be unique.
2) How often do you expect to encounter a specific subtype of a monster in your adventuring career? In 3E you need an average of 260 encounters to reach level 20. How many of these will typically involve bugbears?
A lot depends upon the monster and campaign in question. I know my Living Greyhawk characters have encountered a lot of orcs, ogres, demons, devils, and bears. They didn't fight too many dragons or Yugoloth/Daemons. Since Living Greyhawk is a very decentralized campaign with adventures that are largely episodic and have a large variety of authors, I would expect that is probably as good an estimate as you can find for a random, unthemed campaign. In Red Hand of Doom, however, I remember fighting a lot of hobgoblins.
One thing to remember, however, is that novelty doesn't just wear off for one campaign. I've played in many campaigns and after the third or fourth half-fiend encounter, they're not just dull for the one character in the one campaign who first encountered them. They're dull for all my characters in all my campaigns.
The thing is: D&D has always had such an overabundance of creatures that you'll never have to encounter the same creature twice, unless your DM has a certain favorite or strives for a more 'realistic' environment by restricting himself to a certain subset of monsters he deemed appropriate for his setting.
Except that that just doesn't seem to be the way it works out in most campaigns I've played. In all current and previous editions of the game, there are small subsets of monsters that are more common than others. As a hypothesis, I'd guess that, like the top 10% of wage earners pay 90% of the total tax bill, the top 25% of monsters in the monster manual probably account for 90% of the total encounters.
In the case of the bugbear strangler the main problem is that there doesn't seem to be any supernatural or magical effect involved in the maneuver, thus leading an observer to the conclusion that anyone should be able to learn the maneuver.
If the maneuver had some obviously otherworldly quality to it noone would question its uniqueness and accept that only bugbear stranglers are able to do it.
That's a separate but related problem. A one or two trick pony design philosophy strikes me as problematic for monsters in general for reasons partially explored above.
It's related to the problem of the manuever's uniqueness because the uniqueness of the manuever separates it from the ordinary field of play. A monster who is good at grappling is a grapple monster. He has his specialty but doesn't do anything fundamentally different from the rest of the monster manual world. A monster who has unusual and unique abilities when grappling differs in some significant way from the rest of the monster manual and requires unique strategies to take it on.
On the other hand, there is also what I think of as the angry bear effect. In one Living Greyhawk module that was written unusually badly, there was an encounter with a pair of bears who were "so angry that calm animals and calm emotions won't work on them." As a friend of mine said after judging it, "my barbarian would like to get so angry that hold person doesn't work on him, but all he gets is +2 to his will saves." There are things that characters might reasonably be able to expect to do and if the rules just say, "you can't do it, that's a unique ability of the bugbear strangler" it damages the consistency of the game.
For that matter, "I'd like to be able to do that" isn't the only way that a unique ability/exception based design philosophy can ruin the consistency and flow of a game. When I recently ran the Daednu demon from the Monster Manual V, I used it's ability to leave one of its flesh-hooks in a target and immobilize the target because the flesh-hook pins the target to the ground. The monster specifies that you need to succeed at a pretty high DC strength check to get un-immobilized. My players' first reaction, listening to the description was, "I want to cut off the flesh-hook that's holding me to the ground and pursue the demon." Being a sensible DM, I allowed it, but the ad-hoc rules I came up with for doing so were not particularly good and the party's cohort mage just dimension doored them off of the hooks and into attack range of the demon.
The point is that any unique ability/exception based paradigm will inevitably produce a lot of results where the designers don't properly anticipate and account for all the likely means of dealing with those abilities and since they are essentially ad-hoc abilities that work "because Mike Mearls says so" the DM is on his own for adjudicating the extenuations.