As many readers of this site know, there exist in the Pokémon video game community several banned moves and items, ostensibly to make the game rely on "skill" over "luck." However, in a game where critical hits occur every so often and many attacks have higher than Swift's 0.4% (or 1/256) chance of missing, what is the purpose of this? I'll tell you: It's because people don't like it when the game doesn't roll numbers that they like.
Luck is an integral part of the game, given that the game has a random number generator. It's through this luck that the game is made interesting. Do you run Fire Blast, with its lower accuracy than Flamethrower, in the hopes that you're going to beat the odds and land it enough to do higher damage over time? Do you bank on your opponent being fully paralyzed two turns out of the eight you need to set your combo up? This is where skill comes from. In other words, skill comes from manipulating the odds to be in your favour.
Clearly, if something like Double Team is going to be a powerful strategy, shouldn't anyone who wants to win use it? Well, yes and no. Double Team is a powerful strategy. There's no disputing that. However, let's take a look at what all you can do in response to it:
The basic arguments against Double Team are as follows: "It's annoying," which is followed by its corollary, "I don't like to play against them," and the second argument, "I don't like it when I have bad luck." As anyone who's played the TCG—and for those of you who haven't, count yourself lucky—for more than ten minutes can tell you, bad matchups are part of the metagame. Two stall decks playing against each other is an excruciating thing, for instance. But yet regardless, the more skillful player will prevail, and life goes on. Nobody bans stall decks or combo decks because they don't like playing against them. The same principle holds for the video games. If you play long enough, odds are a 90% accuracy attack whiffing, or an inopportune critical hit, or whatever is going to end you. This is luck, and it's a part of the game. Double Team is annoying, but it isn't the be-all and end-all even in a metagame in which it exists.
The presence of luck is also very healthy for the game as a whole. While the more skillful player should win more games overall, it's unhealthy for the more skillful player to win 100% of his games, as that results in a stale metagame where the winner can basically be decided without playing more than a few rounds. Luck allows anyone to have a decent chance of winning, even if infrequently. In Magic—which I'll be using as an example instead of the Pokémon TCG since it's the better game—this manifests largely in the shuffling, i.e. with manascrew and so on. In the video games, this manifests in high-accuracy attacks whiffing and critical hits at the right time and so on. These are not unfortunate parts of the game, to be explained to newbies as, "Occasionally your attacks are going to be critical hits. It's sad but there's no way for us to remove this heinous feature." These are parts of the games that exist to add variety to the game, to allow anyone to beat anyone.
Shouldn't a player with the superior strategy prevail the majority of the time? Isn't that what all the "competetive" battlers are saying? If Double Team isn't countered, then odds are it's going to be the superior strategy. If the Double Team user's opponent starts packing counters, they're going to falter, and quite possibly lose. Many of the counters to Double Team work well against other strategies, resulting in a team that doesn't have to be specialized in order to win. It's only due to player laziness and gross ineptitude that none of these strategies are even attempted. As a result, we get the image of Double Team as some invincible god move that turns the game into a "who can hit first?" fest. In reality, it only gets this way if you don't even try and get around it.
The same holds true for OHKO attacks, which are similarly banned by the self-styled cool kids. You can expect to KO something once every three turns, on average, barring Double Team or other accuracy-modifying effects. If you bring in some kind of Lock On->Horn Drill style strategy, this increases (assuming nobody switches) to once every two turns. Many physical sweepers are set up so that they're going to outrace at least the unaided OHKO attacks over time. It's a simple bit of statistics. Banning only needs to occur when the game state becomes truly degenerate, e.g. when a strategy becomes the only strategy even worth considering. Double Team and OHKOs are powerful, but they're not that powerful unless you're totally unwilling to play against it. If you're not going to even try to play against a strategy, you deserve to lose to it.
Smogon claims that they're better than the secretive TCG players, who hide their strategies and findings. Yet when directly pressed for some kind of statistical backing for their arguments, even something as simple as "a Double Team user on this team makes it win X times against team Y, as opposed to Z times when lacking Double Team", they come up short, instead falling back upon such rhetoric as, "Well, we're Smogon. We're the best. Just listen to us!"
At least Azure was respectable. They probably did the right thing in not carrying on into the current generations—this way, they'll never ruin their credibility. While we'll never see the brilliance of Cat-Gonk, Meowth346, White Cat, et al. working together in one place again, at least we can rest assured that the equally-respectable Smogon has taken the mantle.
Oh wait...