A big issue is that when SS began, and you got benefits at age 65, the average 65-year-old had a life expectancy of 5 more years. Now it's 20 more years. People are drawing benefits for a long time. What if they keep lengthening lifespans?
The scenario in the OP is particularly relevant to me as it's the exact situation my father is in. My mother died, therefore her SS check stopped. His expenses did not go down by $800 a month, but the income sure did. He worked decades for a big company who froze their pension plan 6 years before he retired, which kept his pension check from being 40% larger due to the formulas used.
He did nothing wrong, did not live extravagantly in any way (one vacation in 30 years), but he simply cannot continue to live on his own on one SS check and a small pension.
What I learned from his situation is that a "good middle class wage" and its associated SS benefits cannot stand up to decades of even low inflation. His pension is not COLA, SS increases do not keep up with actual cost-of-living for retirees. They were doing fine when he first retired - both SS checks and the pension allowed some little luxuries like eating dinner out on Sundays. Yet even before my mother passed, they were struggling a little, the dinner out on Sundays had long been stopped. Decades of retirement really take a toll.