I'll accept a couple premises. I will accept that lower-powered characters are frequently better roleplayed. But that has a lot more to do with the fact that there's nothing else to do with a weak character - when all you can do to achieve your goals is roleplay, you either roleplay or fail. But it mystifies me that some people think that this somehow implies a subsequent lack of roleplaying with more powerful characters. It doesn't logically follow. And "in my experience" isn't a valid argument. Game with me. I'll change "your experience."
I might go so far as to postulate that more powerful characters can be every bit as much a roleplaying challenge. A weak character must be roleplayed through conflict. A powerful character doesn't necessarily have to. With a powerful character, there is definitely a path of least resistance. Roleplaying a powerful character well often involves taking the harder path - in other words, it can be more challenging.
Anyway, power does not equal twinkery. I will write an extensive post proving that power level doesn't inherently equate to twinkery, that it doesn't have any particular quality that exists independently of the player, if you really think it's necessary. For now, I'm operating on the assumption that you're all smart enough to understand that the power=twinkery notion is really based on the idea that power level is an indicator of twinkish tendencies in a player.
Here's what gets to me, though. The fact that it's frequently an indicator of twinkery does not necessitate that a powerful character be played by a twinkish person. In fact, assuming so is basically buying into a stereotype. I can make a bunch of claims that most of the White Wolf players I've known were angsty little drama-goths, that most of the D&D players I've known were socially retarded computer nerds, and that most of the LARPers I've met were whiny little metagaming bitches, and probably do so convincingly. But most people will accept that those are stereotypes, and, even if they are indicative of most such gamers, that it doesn't logically necessitate that all such gamers are like that. If I tried that, my participation in an upcoming vampire LARP would make me a whiny, angsty, metagaming, drama-goth bitch. Usually, even the people who say stuff like that are aware of the fact that they are citing stereotypes based on personal experience and opinion.
But people will equate powerful characters to twinkish players, and then make an absurd attempt to logically prove, with their own experiences of all things, that one necessitates the other. Or at the very least, they will operate from the assumption that a powerful character is being played by a twinkish player, without it ever occuring to them that they are basing their decisions on a stereotype. It's not even a situation where they will say "I don't like high powered games because they attract twinks," they will say "you play high powered games because you are a twink." It makes no more sense than the snotty stereotypes I listed above, but a lot of people somehow can't see that it's as much a stereotype - just as illogical and inaccurate.
This carries over to characters within games, too. I know a lot of people who would call me a twink based on the characters I've played, just because they're operating on certain assumptions about power levels and game balance. They're all people who've never gamed with me. Those who know me, know better. I once built a character for a game who was so ultra-specialized toward combat, that he outstripped the rest of the group by a huge margin. He had two attributes that exceeded normal human maximums because I specialized his cyberware. The GM allowed the character because she has gamed with me for about six years and knows very well how I roleplay. None of the other players had a problem with it either. It was a new character in a game that had been running a while, and apparently I'd earned their trust.
What twinkery is really all about, though, is the intent of the player. A player who only wants to play a "look what I can do!" character, or a player who always has to "win," can fuck up a game right quick. But for a player who is genuinely interested in play a good character and telling a good story, the only relevancy their power level has regards the attitudes of the GM and the other players. Such a player could effectively play a god and not screw up the game. And for the people who want to say that this latter type of player doesn't exist, who want to use phrases like "I've heard all the justifications before," I'm going to sit and tap on the word "stereotype," written several other places in this post, until they get it.
With that said, I do always respect the power levels a GM sets for their game. And I don't always allow high-powered or imbalanced characters in my games. But for reasons other than "twinkery."
Sorry this was so long. It's something that's been building up for a while.