I think you've got things a bit off. I think more correct ones are:
- "This country became a world power with 76 million residents in 1900 before it got any of the Progressive era administrative state."
- "The country became a world superpower with 180 million residents in 1960 before it got the modern administrative state"
You wrote "world superpower", but the US didn't become a world superpower until WW2, well after ~1915, which is when the population reached 100M.
While the US started becoming a world power in 1898, with the Spanish-American War, and fully became a world power by WWI, that was after the Interstate Commerce Commission was formed in 1887, as the first administrative agency.
Now, you wrote "modern", which of course is in the eye of the beholder and likely is meant to exclude the ICC. Did the modern era start in 1906, with the FDA and the Federal Meat Inspection Act? Or Wilson, with the Federal Reserve (1913) and the FTC (1914)? Or the New Deal (1930s), like the SEC (1934)?
You'll note that all of those were before the US became a modern world superpower, and several before the US population reached 100M.
On the other hand, this beholder - https://ballotpedia.org/Administrative_state - points out that the modern administrative state didn't start until 1964 with Johnson's Great Society programs.
Here's another equally true statement:
- "The country became a world superpower with 203 million residents in 1970 before 18 year olds had the right to vote."
While true, that wouldn't justify removing the franchise from modern 18 year old.
Your observation, even when corrected, seems to be similarly weak as an argument to remove administrative agencies.