The main reason heart disease and cancer are the leading cause of fatalities is that we're so good at fighting infections and other diseases that we're living longer.
First of all, the overall mortality rate from all causes decreased by 54% between 1900 and 2010 in the US, so that's awesome. But also, back in 1900, the mortality rates for pneumonia/influenza, gastrointestinal infections, and tuberculosis were ALL higher than rates for heart disease. Today, improvements in public health have dramatically reduced the risk of dying from TB, pneumonia/influenza, and gastrointestinal infections in the US. Modern medicine already saves countless lives, and it continues to improve.