We do not remember what we did in our past lives and what we are being punished for. We don't decide where to born, who will be the parents, relatives and lot of other things? If People do really bad deeds, they should get punishment in the present life, not in the next birth. At least they will realize that they did wrong. Getting a new body & soul and paying the past karma is not the solution. If somebody has done very bad and spoiled somebody's life and if we don't see him/her getting punishment for that in the present life, the suffering persons life will be waste. Then its a Endless journey, doing bad/good karma, coming again and again in this World.
Karmic balance is associated with the soul, not body. Multiple births are a means to start afresh - you are born as a child, having no undesirable qualities like ego, greed, etc. So this is an opportunity given to your eternal self to now engage in the welfare of the society and do good Karma. Most people again fall prey to ego, lust, pride, etc and hence keep cycling in the birth/death process.