Absolute power corrupts absolutely. Petyr Baelish avoids this corruption by avoiding the source of power, but staying close enough to bath in its benefits. 'You can identify the most powerful man in the room easily, but the smartest? You have to look to the source of the power for that. The powerful man may speak the most, but who does he look at the most? This look is important, it is a pursuit of validation. This look will be directed towards the smartest man in the room. The snake in the grass.' Petyr Baelish is that man. This is why he succeeds to the degree he does.
Finally, someone outsmarted this snake. Arya would have been an innocent pawn, likely grow up just like her father Ned Stark. But with the cruel twist(s) in her life, she received the training on her life. And able to double-edged this baddie.
We can all learn from this. The world is not fair. We should learn how to fight the banks, the cleverly hidden corrupt system.
There's a dedicated top cop who exposed everything the govt did in the documentary "Collapse". Yet the majority still weak since by greed (by capitalism) they thought they will have a chance to join the 1%.