Do people consult doctors to obtain medical leaves shorter than a week? It seems like a waste of time for everybody involved. Either the problem is bad enough that you need time off and you might as well round it up to a week, or the problem is benign enough that you don't need time off at all.

That's the whole point, before they would only need to do it on the fourth day of sickness, now you need to go to a doctor on the first day. More workload for doctors and either sick people coming to the office infecting others, or getting the whole week off immediately.