I think that what you're suggesting would be fairly complex to implement. I understand the reporting of adverse events associated with drugs to the federal government, and I think it makes sense when the federal government is approving these drug products.
I'm not a physician and so can't comment from a strong knowledge base, but there are many types of cancers. How would they be associated with a particular cause?
I think there are many details associated with what you're suggesting that would make it a very complicated proposal to implement, but it's certainly an interesting suggestion.