You can get this right now in many state university systems in the US if you want it. Especially in the case on non-exempt employees. Unless the employee does something criminal I would say it would takes a minimum of a year to fire someone but probably more, and with clever enough employees it can be nearly impossible. Because of seniority and the like it can be really hard to layoff a specific employee even when there are budget cuts that eliminate positions.
Here's the problem. Bad employees tend not to leave of their own free will, in my experience the worse they are the more this is true. However, really good employees tend to move on every few years as they grow into new opportunities. What this means is that every time you replace a good employee you roll the dice that you'll get a bad one. There is now one position that is likely locked in place with bad employee. Over time this leads to a lot of bad employees, which in turn lowers your retention rate of good employees.
Now there is a standard tactic to fight this (and this same tactic would work in your senario as well). Make the bad employee extremely uncomfortable. Within the rules of the system do everything you can to make work suck. This does work reasonably well. The problem? Terrible employees are immune to this. So if this tactic is abused you end up with only terrible employees.
So in short, without the ability to fire people easily you tend to go on a downward spiral of increasingly bad-mediocre employees.
It absolutely can, and as noted even if it works you still run into issues.
The overall problem is that in the end it becomes a game between bad employees and the management see how can play the rules against the other the best, which is a phenomenal waste of time and energy.
Improve your recruitment, hire good people. Take advantage of any probation period. In the UK this is generally 3 months, and can be extended. During this period employees are just 'at-will'.
In the UK it can be up to 11months and 3 weeks before the main employment laws kick in.
Here's the problem. Bad employees tend not to leave of their own free will, in my experience the worse they are the more this is true. However, really good employees tend to move on every few years as they grow into new opportunities. What this means is that every time you replace a good employee you roll the dice that you'll get a bad one. There is now one position that is likely locked in place with bad employee. Over time this leads to a lot of bad employees, which in turn lowers your retention rate of good employees.
Now there is a standard tactic to fight this (and this same tactic would work in your senario as well). Make the bad employee extremely uncomfortable. Within the rules of the system do everything you can to make work suck. This does work reasonably well. The problem? Terrible employees are immune to this. So if this tactic is abused you end up with only terrible employees.
So in short, without the ability to fire people easily you tend to go on a downward spiral of increasingly bad-mediocre employees.