There are several reasons you might want live power monitoring:
If you insulate houses for a living and want to prove that the heater is switching on less often (paying off the cost of the insulation) you want live power monitoring on that one circuit. You can then correlate the power saving with outside temperature and time of day.
If you run office buildings, real time measurement can help you localise faulty HVAC units. It can help you find out when the lights are on and they shouldn't be. It can tell you that there are a lot of standby loads being left on overnight.
If you have a typical house and a huge power bill, you might not know which of many complex loads is using the most power. Perhaps it is standby devices. Perhaps it is lighting in the kitchen. Perhaps the fridge is leaking and turning on more often than it should. Maybe it is the hot water. Once you have localised the problem, you can make a smart investment to save power.