Employees don't want that. The terms of the current relationship are centered around the employee's desire for continuity and stability.
Most employees do not want to be tied down to the company in a binding fixed-term commitment; how much worse would things be if people weren't free to pursue other employment whenever they wanted? How much more abuse would employees suffer if they didn't have the option of walking out and finding comparable employment at any time?
Most employees want benefits and perks that would be very difficult to provide in the context of independent agency, like medical insurance. In professional circumstances that are based on procuring such agents, there's usually a union, co-op, axis, or league that furnishes the benefits the worker desires. Read this page [1] about the stability NBA players lacked prior to unionization.
The grass is always greener. Perhaps an employee's raw salary would be higher if a free agency model was used, though I personally doubt it would be, but most of the terms of this game are defined by the employee, not the employer.
A world where every employee is an independent agent with his/her own contract is a much, much different world than we have now and would take a long time to analyze with any depth or completion. It's not that there aren't ways to make it work, but the standard employment relationship exists because it's the employment arrangement most conducive to the type of lifestyle the average person wants to have.
[1] http://nbpa.com/about-nbpa/