I agree with your premise that politics is a result of the power structure of society. But I don't agree the difference between the left and right is one wants top down power, while the other wants bottom up.

American politics started with different interpretations of the founding father's principles: rule of law, personal freedoms, written contracts, democracy, and the limited role of government. The right thought these ideas were universal, while the left thought they develop over time.

This led the right to be 'Modern' universalists, while the left became 'Postmodern' relationalists.

This aligned the left to Postindustrial society, while the right aligned itself to Industrial society.

The right are capitalists, while the left started as socialists and in recent years (since Clinton) have become corporatists.

This idea that the left wants distributed power is false if the left has become corporatists. The left and right would both be "right".