You missed some downsides: anguish, more tests for something that isn't a problem, costs, possibly suicides. You may want to read up more on the downsides to breast cancer screenings for reference.
I didn't delve into all the downsides, but I did mention the stress and related depression that could be associated with a false positive. I also noted how there are downsides to mammograms, such as a breast biopsy. We could go a step further and note that some women opt for mastectomies as well, especially for genetic screening (BRCA).
There's plenty to delve into regarding the risks and benefits of screening tests: Here's a good framework for those interested.
