The problem with your entire theory is your assumption that any of these diseases would be weeded out by natural selection.

Natural selection only comes into play in determining which animals will BREED and which will die before they do so. The incidence rate of cancer in the human breeding population (say, under 40) is very very small. The 'inferior' genes have already been passed on to their offspring by the time they are affected in the slightest by any of the illnesses you mentioned.

Why does a herd of deer become cancer-ridden if it isn't thinned? The animals LIVE LONGER. What we are seeing here is not the degredation of the human genome, but rather the EXTENSION of human life far beyond what was possible 20 years ago, and beyond the limits of the human body without modern medicine.

Also, your assumption that mutation and abormalities are bad completely contradicts the whole theory of evolution and natural selection. Who is to say that those predisposed to cancer are not superior to other humans in some factor (skin tolerance to UV...), with that unfortunate side effect?

Quite frankly, there's nothing natural about what you think should be done. Natural selection in humans cannot be based on any natural factors, because we no longer need to hunt for and aquire food, nor find shelter, nor fight for dominance.