The Future of Human Lifespans: Is Evolution the Solution?

What if we didn't have to grow old and die? The average American can expect to live for 78.8 years, an improvement over the days before clean water and vaccines, when life expectancy was closer to 50, but still not long enough for most of us. So researchers around the world have been working on arresting the process of aging through biotechnology and finding cures to diseases like Alzheimer's and cancer. Assuming the human race is evolving, wouldn't lifespan grow with human evolution?