There is one shining result in mechanism design, a subfield of game theory, called the revelation principle. It says, simply, that if one doesn't like how the game is played, one may design the game that they want folks to play, and offer incentives accordingly, and people will play the game according to the incentives.

While this may sound like academic bullshit, it is the closest thing you'll find to a solid philosophical foundation for why proof-of-work or proof-of-stake systems should be expected to work in practice as well as they do.