Then make your point using real examples, not made up ones ignorant of history that end up blunting your argument.
Yes, Louis XIV didn't have internet service. Does that make the Sun King poor?
Clearly, no.
The usual way to do this through something like measuring the cost-of-living - the US started gathering this information during World War I. Your $100/month now corresponds to $6.50/month in 1920, says https://www.usinflationcalculator.com/ , or $78/year.
We can look up actual numbers. From the Bulletin of the United States Bureau of Labor Statistics #357 at https://babel.hathitrust.org/cgi/pt?id=uc1.31158004110184&se... dated May 1924 and covering the years 1918-1919 we can see breakdown of expenses for different places in the western US:
In Butte, Montana, the poorest family (1 out of 102 surveyed, with 4 people) made $900-$1,200 per year, and had $1,022.50 in expenses. (see page 14). Of that, about $900 was spend on food, clothing, rent, and fuel/light.
In the gold rush town of Cripple Creek District, Colorado (page 22) one family of 80, with 3 people, made under $900, and had expenses of $853.
In Trinidad, Colordo, 2 of 78 families (average of 4.5 people per family) made less than $900/year, and had expenses of $973.
And these are the poorest of the poor! They are in the city, which does affect the numbers - farm living can be cheaper, but surely not by a factor of 10.
So the idea that $78/year was in any way representative is clearly low-balling it by a lot, even if you only meant for a single person rather than a family.
The tables show a 1920 far different than the world you are thinking of. Look at the miscellaneous items for those in the Western states making at most $900/year, at https://babel.hathitrust.org/cgi/pt?id=uc1.31158004110184&se... . 72% of them had life insurance, 11% paid membership to social clubs, 50% paid for movies, 89% got a newspaper, 78% paid for a physician, 22% paid for glasses, and so on.
If 1920 is your comparable, then in 2023 you also need to pay for those, on top of lodging, food, heat, and furniture, for your $100/month.
I have no doubt there were a handful of people in 1920 who lived on $6.50/month, perhaps living by themselves in the back-country of Alaska, but that will be on the extreme low end, far below the baseline of nearly everyone living in the American West a hundred years ago, and hardly representative.