That works for European employers, it's much harder to fire someone in general than it is in the USA.
When a manager finds out someone is leaving, one of the following happens:
1) They're fired on the spot and escorted from the building;
2) The manager tries to guilt them into staying;
3) A pathetic counter-offer is made (nevermind that the reasons for leaving may not have anything to do with compensation);
4) A significant counter-offer is made (usually intended to keep the worker there just long enough to hire a replacement).
Occasionally what you describe happens. It's rare in my experience. Look at it from the employer's point of view; to this point in the employee's time there, they have been able to do pretty much whatever they want w/r/t the worker. No binding job descriptions, arbitrary re-assignment, (for exempt employees) forcing them to work 60, 70, 80 hour weeks with no extra pay, making them do the work of three people for a single salary, etc etc etc. The playing field is heavily tilted in their favor. So, it comes as a shock and an insult when the employee exercises the one right that US workers really have: They can quit. How DARE they! Don't they know that the company will only make 6 bazillion dollars instead of 6.5 if they leave? WON'T SOMEONE THINK OF THE SHAREHOLDERS!