World of Darkness is quite possibly the best game system for ease of inverting. My daughter was in the habit of picking a Flaw and designing a character in such a way that it was an Advantage - and she made up great backstories for them. My shtick was to twist the standard assumptions about various sorts of characters - for a while I played a pantheistic member of the Celestial Chorus, and I was designing a quantum-physics-based Dreamspeaker when for various reasons we dropped out of the LARP group.
(Interestingly, the March 2018 issue of Discover magazine has an article about the possible quantum basis of consciousness that fits perfectly with one of the two possible paradigms I came up with for a Quantum Dreamspeaker. And definitely doesn't contradict the other one.)
Not that other game systems can't be inverted. In 4E D&D, I figured out that if you want to build a really good, powerful Barbarian, the character class you should pick is Cleric... and I also built a semi-pacifist Wizard. (Semi-pacifist in that there's a geas on him against doing damage to any person with magic. But he does use a staff, and know show to thump heads with it.)