The NHS has finite resources. They have to decide if implementing a screening program is worthwhile or not, versus spending the money elsewhere. You can still go to your doctor and get a mammogram (or even a more useful test) if you have other reasons why this might be justified in your situation. They aren’t ‘banning’ mammograms for young women.
Any sort of treatment is invasive. Almost all form of medical treatment has side effects and risks.
Finding out you have "cancer" is traumatic and extremely emotional, though breast cancer is one of the most survivable (in part because, well, everyone loves boobs. Prostate cancer, on the other hand...)
Putting these tools in the hands of medical professionals is one thing. Putting them in the hands of the general public is beyond irresponsible.
People physically assaulted doctors and nurses for not being given ivermectin; imagine how insufferable people will get when some website examined their mammogram and said they have cancer.
