How would improved diagnosis bring down the price of medicine? Medicine doesn't only consist of diagnosis, there's also treatment and infrastructure. It's obvious that any improvement in diagnosis of illness cuts down on misdirected treatment and improves public health, saving money would be a secondary effect.
Besides, the fact that healthcare in the US is so expensive compared to the rest of the Western world is due to political reasons; we know how to bring down the cost of healthcare here without affecting outcomes by doing what the rest of the civilized world does.
