Why? What's the point? A lot of people who were sick, will be healthy. What other outcome should we even care about?
A lot of sick people being healthy isn't the only outcome to consider. Let's suppose that a cure is developed, but it is VERY expensive--let's say $10,000,000 per person. Currently, somewhere in the neighborhood of 500,000 people die from cancer a year, so that's $5 trillion per year to cure them. That's a lot of people, but is it worth 1/3 of our GDP and over double the government's current spending? Even if it was only $1,000,000, it would still cost $500 billion. Is that worth it? That's a lot of other people that would go without help, or jobs, or whatever.
Here's some more hypotheticals: suppose the cure required some component that could only be obtained from other people at great personal sacrifice (perhaps a limb, or vital organ, or even their lives). Would that be worth it? Or instead of people, curing one person required the death of hundreds of animals? Or perhaps it caused significant environmental damage? Of course, these hypotheticals are very unlikely, but the point remains. Making sick people healthy is a noble cause, but it will come with a price of some sort. This may seem cold and heartless, but if the price is greater suffering overall, then we need to think about whether it is worth it.
The populations effects of curing cancer is similar to curing heart disease. These are the number 1 and 2 killers of the elderly. There would be a population explosion as a result. Strictly looking at the elderly, this population would outstrip the youth. The elderly use more medical resources and drugs which would put a strain on economic resources to pay for those same resources and drugs. Compounding this, would be that this same elderly population are retired, they wouldn't be "productive" members of society. Meaning, they wouldn't be the firemen, policemen, etc. that help make society what it is.
Of course, if we found a cure for alzheimer's and arthritis, that same elderly population would be able to go back to work and be productive members of society. They would be generating taxable income to help pay for the healthcare burden, too.
Is it worthwhile to seek a cure for cancer. Of course it is. At the same time, lets find a cure for other diseases, too.
This is the point I was trying to make with my first post. You said it better. However, there is one issue with your second paragraph. Good luck getting the elderly who've been looking forward to retirement for 30 years to go back to work just because you cured their arthritis. Most people start their career with their sights set on retiring aroung 65. Do you want to work until you're 80? 90?
As you pointed out, the elderly population will be larger than the younger population. That, along with their greater experience at organizing and getting things done, and their greater amounts of time and energy to devote to causes, will make it impossible. As it is, AARP has a lot of power for those reasons and opposes any legislation that takes anything away from the elderly or requires any more sacrifice from them. They don't seem to care that it's their children and grandchildren who pay the price. Imagine what they could do if they had even more power by having the majority of the population with them. You would never get them to back to being productive.