And the thing is, the question of whether to negotiate only comes up if you find yourself in the 1% who get to that stage. It's very expensive for a company to find that 1%, and once they have they don't want to go back to the drawing board, and that's just the tip of the iceberg of your leverage at that point. Of course you should negotiate. What have you got to lose?
It doesn't matter how saturated the market is. It's takes time to filter out all the candidates. Labour and opportunity cost via delays and distraction