Maybe for more cureable diseases it would be justified, though?
I'm skeptical. In first world countries, if the disease were more curable, there are already medical test recommendations. For instance, people take routine breast cancer, testicular cancer and colonoscopy screenings. Even there, there has been some findings that the higher rate of testing can create more problems with false positives and the test itself than is really saving lives at the margins. In countries without a national health insurance, money can be an issue to get care as well. In some parts of the world, even if you knew you had something, there's not much you can do about it. Money is often an issue as well as the availability of medical facilities. There would have to be some kind of showing that alerting people would be doing more good than harm.