I read something about 10-15 years ago about this and the author said, despite this type of medical technology, anti-aging doesn't mean immortality. He proposed even if you stopped or reversed aging, you could only live to be about 300 years old. At that point, something would get you: murder, plane crash, illness, etc.
While I'm not an expert on the topic of society and the rise in violence, poverty, etc. I do believe overpopulation does not help the issues. The details, I speculate, could be desperation in the face of poverty, shortages of food/water/fuel, and yet we just keep breeding while we live longer. This would bring the death rate so low compared to today's standards I'm sure we would surely test the viability of our natural resources. We would either be living on top of each other as the population booms and be at a higher risk of disease outbreaks or we would invade the farm land and decrease the production of food which would only be in higher demand. Maybe the issues at hand are not as bad as I think they are since information of them spread so quickly in the information age. I'm not making changes however because I'm human and a clinician that promotes health and I have a son and another due any day.