If they offer average pay, they'll get average employees. If they offer above average pay, they miss out on exceptional employees. And if they offer exceptional pay, they'll likely go bankrupt as most of their employees will not be exceptional.
Negotiation exists because there's no objective way to evaluate the value of the employee to a company before they've been hired. If someone can get twice the work done (and can demonstrate this), they can justifiably demand twice the pay. Of course, the subjectivity is a double-edged sword, because it means that individual prejudices can affect the hiring process.
One way to solve this problem is to handle all negotiation through a well-defined algorithm. The would-be employee shouldn't even interact with a person for this part of the process, just with a webpage. Strong AI is obviously impractical, but you could probably do a pretty good job of predicting performance if you managed to trawl a big enough dataset for some key statistics.
Another approach is what this poster suggested, where pay (above a base salary) is determined by one's peers. In that case, the individual prejudices are averaged (which ideally negates them), and the valuation of the employee is done by their peers. You'd have to be very careful about how you implemented it though, as you run the risk of creating some major social/political problems with that approach.