Well greatness is a matter of opinion and influence does not even make it onto my list and skill only at a certain level.
My actual criteria is that greatness is measured by a musician or bands ability to transmit the sacred to people, to channel something larger than themselves that is spiritual, its ability to draw a person into altered states of awarness of the numinouse, of trancendent beauty. greatness for me is a bands ability to play the moment, to be one with the weather, the crowd, with one another, to lose themselves in the isness of the moment and adapt and bend to that so as to express it and find synchroniciry with it... to be played by god even.
But at this point we begin to leave the realm of popular music into deeper territory.
Still pink floyd, the doors, led zeppelin, dead can dance, talking heads could all do some of this but not all of it at a high level.
Oh and perfect music is boring.