Question: Although there are lots of really bad diseases in the world, if we found cures for all of them then wouldn't the world get too full of people because people would only die from old age or having accidents.
That’s somewhat true and part of the problem the current world is having. The population is increasing in size, and if on average, each couple have more than 2 kids, then the population would continue to grow. If we found cure for all diseases, solved starvation, war and natural disaster, what will probably need to happen is limitation to how many children each person can have (similar to the one-child policy in China) and allow abortion of unwanted pregnancy; if that happens, the population will not grow in size.
A serious (already happening) problem with growing population would be the impact on the environment of other wild-life and reduce bio-diversity (variety of different animals/plants..etc). Hopefully we have not harmed the environment too much before that happens.
Again this is a really good question! Good thinking! This is partly true and I see where you are coming from.
However part of the reason why people in developing countries have so many children is because they know that some of them are likely to die of a deadly disease, war or famine before they reach adulthood. Therefore if we were able to prevent war, disease and famine, then people would probably only have an average of 2 children per couple which is exactly the number needed to sustain the population, i.e. keep it flat and not growing.
It’s an interesting question and not one many people like to ask!
It depends on your outlook really, if we have become advanced enough to stop all diseases then we would probably have become advanced enough to sort out problems such as housing, climate change, renewable energy, nuclear proliferation and protected against natural disasters. We could even have moved to space by then!
As it happens, those parts of the world, (the poorest parts) which have the most disease also have the largest families. Whereas in the developed world people have smaller families who live longer. Therefore overall development of underdeveloped countries is much needed, including the eradication of disease!