First of all, clearly people do not reproduce so that their children will find a cure for cancer but for completely different reasons, and most of them are completely selfish. If people think it is so important to find a cure for cancer (or any other problem) they are more than welcome to devote their lives to finding a solution, why does it require the creation of a new person?
And statistically, the chance that this new person will find a cure for cancer is negligible. On the other hand, the chance of that person getting cancer themselves is much, much higher.
If you insist that it is still theoretically true that your child might find a cure for cancer, consider that theoretically s/he could also start a factory that will cause cancer, or be a heinous criminal, or a murderer, or a rapist, or “just” a creep to everyone s/he meets. The horrible option is almost never considered when people decide to create people, whereas the good option is often brought up as an excuse. But what if your child turns out a monster? There are a lot of monsters out there, and they all have parents. It is likely that none of these parents expected, hoped or intended for their child to become what they have. And yet it keeps happening. Solutions to many human problems have not yet been found, but there are endless people who create more and more problems. The statistics are not really in favor of this argument.
In the best case, your child just won’t find a cure for cancer. In the worst case s/he will suffer from cancer or cause cancer to others. And in the most realistic case s/he will be just another person. After all, chances are your child will not be the incredible thing you expected, but just another person in the world. Another mediocre person who will live a meaningless life in a purposeless world. S/he will disappoint and let others down, will get hurt and hurt others, will take advantage of others and be taken advantage of by others, will experience frustrations and frustrate others, will be bored and bore others, will be casual and unnecessary.
Since such a claim is heard often and in the context of all kinds of problems in the world, and since statistically the chances are that the people who will be created will be part of the problem and not part of the solution, ironically this excuse for reproduction results in more victims of the same problems that people sought to solve by reproducing. So in practice this so-called attempt to prevent the problem exacerbates it.
The best way to deal with diseases like cancer, as well as with any other horror that is a part of life, is to prevent it.