If that were true, wouldn't that mean that politicians are in fact acting in a WYSIWYG manner? They roll in, implement policies that people like, say "I implemented this policy because it has quiet support" and the political defence of the policy is average people like it and can't be talked out of supporting it?

If your position is that the average person on the street thinks a policy is a good idea then the politicians involved aren't going to need complex signalling. They're going to say "You all like this policy! The current mob aren't going to do it >:( Vote for me, I will implement it". The sticking point is all the policies politicians implement that are unpopular with the average person on the street and that polie couldn't win an election if they were visibly standing for their actual position.