It’s pretty simple. They are more likely to get sick and more likely to infect those whose care they are entrusted with.

There’s a long history of this type of sanction. If you are a provider or nurse in a hospital who fails to get a measles, hepatitis, or rabies (after exposure) shot, you’ll be terminated for cause in many places.

The reason why recovery doesn’t “count” the same as vaccination is that immunity doesn’t last very long - 60-90 days typically. Some countries, such as Israel will recognize a single Pfizer dose and recovery as immune, if you have a negative PCR test.