Personally I believe that every woman should think about mammograms regardless of age. Yes, mammograms in their 50s are likely to save some lives, but the chance of an individual benefitting is still small. While saving lives is worthwhile, this benefit comes with a cost.
I think women should think of what is more important for them: a small (in absolute numbers) reduction in probability of dying from breast cancers vs high probability of at least one false positive, significant probability of at least one biopsy, and very small (but probably larger than the chance of benefit) chance of overdiagnosis (i.e. increased risk of being diagnosed with cancer).

Personally (I am still in my 40s), I no longer have mammograms. I haven’t yet decided what I’ll do when I turn 50.

The main thing people – doctors and patients alike – should realize is that screening is a choice. It is not an obligation, it is not something responsible people do. It is a personal choice based on one’s risks, preferences, tolerance of anxiety that comes with false positives, etc.