One of my duties when I was an Office Manager was the Benefits Coordinator. While I worked for small offices - under 15 employees, I rarely did anything on a day to day basis. Yearly we would review the plan and get quotes. Now, that does take up some time, but only for a couple hours for a few weeks. Also, the paperwork when a new employee arrives.
It also depends how the companies insurance is set up. Whether they are the actual provider or not. For example, my husband works for a large manufacturing plant and his company is the provider of the insurance, but hired an outside company to manage it. In this case if there are glitches in claims then as an employee he would go to his benefit coordinator to get the issues resolved. However, if insurer is someone like BCBS there would be less issues b/c the employee make all the calls, etc.
I hope this helps. I might have been lucky though in that my employees were self sufficient.