For me the benefits of bouncings(forwarts and backwards) are 3... If the boxer bounces fast enough he uses the elasticity of his muscles. That means that he uses much less energy. If you stay 5 mins on the balls and not moving you want be able to move after that... The secont reason is that the boxer is already in motion. If you are goinig forwarts in your rhythm it will be much faster to trow the jab... The thirt reason is the defence.First If the boxer is getting hit, he will be "softer" target. This means that he will absorb less damage. Second: without a rhythm its almost impossible to evade punches(atleast to the left)... This constant movement gives the oder guy uncertainty and makes the movement of the boxer slightly faste(all the great "head movers" have their own rhythm).
On the oder hand if you bounce you loose some punching power. This comes from the mechanic of the punch. In order to get alot of speed you need great acceleration. This means that you need the biger muscles(gluts instead of calves) to initiate your punch. Thats why all the great punchers have there feets planted.