Rubbish.
In fact, except for payments on the Civil War debt, the Federal Government by, oh say, 1872, was roughly the same size & scope as 1860.
For example, military spending in 1872 was the same percent of GDP as it had been in pre-war 1860 = less than 1%.
Yes, tariffs remained relatively high until 1900, but by 1917 had returned to the lowest levels seen since 1815.
And Civil War income tax (which had also been proposed for the War of 1812, but was not needed then) was abolished after the war, not reinstated until the 16th Amendment was ratified under President Woodrow Wilson.
So, whatever "FedZilla" proved necessary for the Civil War was afterwards eliminated as soon as possible.
"Progressive era" thinking did not become dominant until the turn of the century, circa 1900, and was certainly more popular amongst Democrats than Republicans such as Calvin Coolidge.
What was "established" was the fact that FedZilla could demand to be fed (in money and lives) when it Wanted, and no "consent of the governed" could gainsay it.