No, such limitations would likely be illegal (without additional compensation, beyond the wages, also being stipulated for the period where the employee couldn't leave / couldn't be let go) in many states. I have never seen such a guarantee / requirement in an employment contract, such a "key man" provision would likely be reserved for someone who is in possession of some critical knowledge to the company and company is willing to pay for it.

It's a double edged sword. It's easy to be let go (basically, pack your stuff and get out while escorted by security, just like in the movies), but it also makes it much easier for companies to take a risk and hire you. In Europe, hiring someone is a big risk and companies are extremely careful to hire since they're taking on a big responsibility. As a result, permanently contracted positions are even more common in Europe than the US as a result in my experience.