What about cancers caused by contagious diseases? Happy to immunise against HPV but tough shit if you get cervical cancer, you're on your own.
I live in a country that is sensible enough to have universal healthcare, despite the best efforts of the Liberals (the conservative party in Australia), and am happy to open my wallet to help others. Although I don't actually open my wallet, it just comes out of my taxes. Much like it comes out of yours. Wouldn't you like to get something for the ~$4000/yr of your taxes that are put towards public healthcare? Or are you happy to get nothing for something?