3000-4000W seems to be the desired level of power for a nice boil. This is based on the # of BTUs that it takes to get the desired boil off.
4000W is 13,468 BTUs, 95% of that is 12,965
970 BTUs are required to create a pound of water vapor from boiling temps.
12,965/970 is 13 pounds of water
13/8.34 is about 1.5 gallons/hour boil off
3000W would net you 1.2 gallons/hr boil off
Anything above 4000W is simply a desire to reach temps. faster. If one is looking to go to 10 gallon batches, 5500W and up is a nice thing to have, maybe not needed, but nice for sure.
I do relish reaching a boil in 13 gallons from 50F in 35 minutes. NO it is not necessary, but it was important enough for ME to put in the extra work to do it.