The western states were way ahead of the rest of the country in women's rights. Wyoming, Utah, Idaho, Colorado and Montana were the first to give them the right to vote and hold office. Part of the motivation was because the men wanted to attract the more sturdy women from the east to come out and settle.
And government started growing in those states as soon as women got the vote. And the federal government started growing in 1919. (Not counting the explosion of government during Wilson’s war.