Mortality from breast cancer before effective chemotherapy and surgery (before the 1970s) was high. This is partly due to the fact that before mammography, most cancers were detected by feeling them. At that point a sizable fraction had spread to distant parts of the body, which is almost always eventually fatal back then (and still often fatal now). At the other end of the spectrum, small slow-growing cancers that couldn't be felt probably wouldn't result in death in a short time frame, so women died of other reasons as the life expectancy was somewhat lower then. These second type of cancers are much more common.
The question then becomes, if mortality is not improved by mammography, especially since we are good at treating early cancers, is there a point to doing it? We have good data on the risk distant cancer recurrence (Stage IV cancer) from an analysis of several very large trials. A woman with a <1cm tumor has a 14% risk of metastases and 9% risk of death from breast cancer in 15 years, compared to 19% risk of metastases and 17% risk of death if the tumor is 2-5cm. This is for the most common types of breast cancer, and with all current treatment (surgery, radiation, chemotherapy). The reason this hasn't translated to a survival benefit for mammography is that most tumors are felt before they get to 2cm, and the differences in survival for <1cm vs. 1-2cm cancers are 4 vs 9%.
Overall, most cancer societies world-wide think that mammography every 2 years is sufficient. Probably more important than that is having any changes in your breast evaluated. Most of the women I have seen in clinic who have advanced cancer that is difficult to treat had something they felt but didn't get checked out for several months.
The important caveat to this is for anyone who has a parent with breast cancer. The risk of breast cancer is 2x (25% risk by 85 years old) for these women, and 1.5x (18% risk) if a grandmother had breast cancer. There is likely a benefit to mammography.
TLDR: women with a parent or grandparent with breast cancer probably will benefit for mammography. Otherwise, mammography won't reduce risk of dying from breast cancer but may reduce the risk of needing extra treatment down the road.