Not "clipless" per se, but the point is a secure pedal connection. Despite you and some people's protestations to the contrary, you really can pull back and up through the pedalstroke which is very beneficial during sustained climb at threshold effort.
So basically, the largest advantage, with clipless, is to be able to "go nuts" without worrying where your feet are on the pedal... I won't argue with that.
However, the pulling up phase of the pedal stroke isn't going to and just can't generate much power when compared to the downstroke, simply because of the muscles involved(hip flexors and abdominals). I'm not sure why people think this is particularly so advantageous on a climb? Perhaps people exert themselves more on a hill, something not really specific to the grade of the road itself, thus clipless are an asset to keep their feet on the pedals. As for the "pulling back" part of the stroke that is also done on platform pedals with correct technique.