No.
This is a well known demography/quant sociology/stats problem. Lifespan was shorter 100 years ago, yes, but not by that much. There were PLENTY of old people.
Here's a really good chart to use:
https://www.infoplease.com/us/mortality/life-expectancy-age-1850-2011
You can see how long you could be expected to continue living at any one point in time. So for instance, you could expect to make it to around 65.6 in 1919.
If you made it to 40, you were probably making it to 70.
Lots of things killed you young back then.