The rate itself has no time element so it tells you nothing about the number of people in hospital right now and hence isn't very illustrative of how hospitals can be swamped by this disease.
More interestingly (for me at least) is that the mortality rate is dependent on a patient's access to a ventilator. This means if you caught the virus early in the spread of the pandemic your odds of surviving are substantially higher than if you caught it right at the peak of infection.
This is impossible to reflect in a simple global mortality rate and so really paints a different picture of the virus - the death rate in South Korea vs other places really highlights this.
I guess to your point, hospitals are more in this way because the virus is so infectious, rather than it being a universally dangerous disease as may be seen from a higher mortality rate. Remember, a high number of people experience little to no symptoms from catching this.
This variability in symptoms doesn't seem to be as true for other lethal diseases like say malaria or dengue fever