Cant I just rapidly iterate through each of the leds and turn them on
Not really the refresh rate and the on / off ratio would be rubbish. With an on off ratio of 64 : 1 the LEDs would be too dim. The 4051 has too much internal resistance to compensate for this by boosting the current and all the current has to come from the arduino pins. So while it would function it would be rubbish.