Everyone was worried in the 1970's that the 1990's would have massive overcrowding and famines, but it didn't happen. Instead, the world population growth rate has begun to level off.
Why? In affluent countries, people no longer have children out of necessity, but of desire. In fact, many first-world nations are actually now undergoing population contraction (Japan, much of Europe).
If you eliminate aging across the world, the necessity of children will go away. People will only have children if they want them.