And here I don't understand why a simple "Advantage" is able to cancel a "Threat", while the "incredibly potent effects" of a "Triumph" is not meant to be at least just as powerful, although "Triumphs" are officially described as "positive consequences" (just more powerful ones), just like the "Advantages" are described.
Because the number of Advantage/Threat, Success/Failure, or Triumph/Despair are not consequences or effects, they're a mechanic.
Consequences or effects of actions within the game likewise exist within the game, not on the table in front of the players. A consequence or effect in the game is something that can (at least potentially, or theoretically) be observed by the characters, rather than the players.
Does that help any?
I haven't thought about this way of looking at it. It is kind of abstract, but it makes a lot of sense. The consequences or effects, as you describe it, are not mechanical events you see on the dice, but are something you "describe" by interpreting the dice while resolving the dice-results. English is not my first language, so I ask: Did I understand you correctly?