I saw the Joe Rogan clip[1] and I agree that Michael Osterholm's analysis of this seems correct when it comes to the United States.
Denmark however has a completely different structure socially. All private sector employees who can work from home are urged to work from home. All public sector employees who are not working in any matter-of-life-and-death function are forced to stay at home. The public sector employees will still get paid despite not working. Practically this means very, very few cases of health care workers with children needs to be home supervising the children.
Wait, how would this prevent health care workers with children from needing to be home? Who is going to be watching those kids while the parents are working at a hospital?
There might be some cases where watching the kids for them is difficult, but most likely the local hospitals already have an idea for this for the minority of employees whose single parent or both parents work in healthcare. Usually their partner can help out.
How about keeping the daycares open for the children of those in healthcare and only for them? Still a big spread reduction, zero healthcare side-effects. It would be very difficult to enforce because so many others would think that they deserve an exception as well...
Most children have two parents. The few cases where both parents work in health care they most likely have immediate family and/or friends who are either public workers or private sector workers who can work from home.
Denmark however has a completely different structure socially. All private sector employees who can work from home are urged to work from home. All public sector employees who are not working in any matter-of-life-and-death function are forced to stay at home. The public sector employees will still get paid despite not working. Practically this means very, very few cases of health care workers with children needs to be home supervising the children.
[1]: https://youtu.be/cZFhjMQrVts