Also once you are up and about at altitude one side can maintain cabin pressurization up to service ceiling but too tough an ask to do it from the ground up to FL410.
A single pack is easily capable of presurization from takeoff to cruise.
The MEL is about planning to operate with a know system deficency, whereas the QRH is about operating with a systems failure during flight.
The MEL infer a "risk management" for planned single pack operation V the QRH and the likelyhood of a second pack failure in the case of one pack failing in flight.