Not all employers want to pay as little as the candidate will accept. I can state this as fact as I am an employer and I do not do that.
As an employer, I want a happy and loyal staff member. Negotiating them down on price doesn't achieve that. I have never offered less than someones initial asking price, and sometimes paid more.
I think it's wrong to assume the employer and employee have differing objectives. We hopefully both want a successful relationship/partnership. Achieving a salary that both are happy with is part of that.
As for your example, again you assume that the employer makes an offer or the employee demands something. Can't it just be a discussion to find the most appropriate salary? That's how I do it.