This has been an interesting thread. I didn't think I would hit so many nerves with the question. As an original act, we only play 45 minutes. People in the audience probably have not heard the songs before, or if they have, maybe once or twice.
In my mind, energy is contagious. If the band has energy, the audience tends to sit a little more on the edge of their seat. They participate more. If the audience never smiles or never makes eye contact (that's right it's fake because the lights don't let you actually see them, but they don't know that) they feel like a spectator and not part of the show.
Watch The Voice on NBC. Not one of those singers after the blinds, just stands there. They all move across the stage, they all interact with the audience, they never just sit there. You can watch any live DVD (or actual show) of any famous band, and the show is hugely important. It's not just the music. Anyone old enough to remember The Cars and how they basically just stood there and played the album note-for-note. They were considered a horrible live act. The music as perfect, but no one felt engaged.