You're dead right in that politicians are greedy assholes.
They want to win elections and to do that they need votes.
What would the republican party do if they'd lost miserably in every election in the last decade? Obviously they would shift their policies to the left in order to be more popular.
What would the democrats do if the republicans moved to the left? Obviously they would have to move further to the left to minimise the votes lost to the republican party.
As the population votes on the left, political policy moves to the left. This seems so plainly obvious to me.