it was a sensible doctrine in 1823, and we see 40 years later in 1864 the French under Napoleon III still attempted to install a Hapsburg as Emperor in Mexico.
The definition of a sphere of influence is "a country or area in which another country has power to affect developments although it has no formal authority."
And “the Mexicans” in this context were an expansionist Spanish colonial empire too.
What do you mean by this? The Philippine War started in 1898 in Cuba, and began US world expansion. If you're dating expansion over the continent as overlapping with that (which you should) you're agreeing that there was unbroken expansionism.
edit: and what does Spain's (or France's) empire have to do with anything? If I burgle the house of a burglar, it doesn't make me not a burglar. The question was whether the US was expansionist, not a moral judgement about the people who controlled the places it expanded to. You can't say that we weren't expansionist and also that they deserved it.
To be clear it's not that you're in a burglar's house, it's that you're robbing the same place.
That is not entirely true. The United States government and/or its citizens acting autonomously had global reach much earlier than 1898.
Throughout the nineteenth century, American expansionism was seen in various Central American countries, Ecuador, Liberia and Japan, for instance. In some cases, like in Japan and in Brazil, America’s aggressive policies were thwarted. But it does not mean that there was not expansionism.
Spain lost the vast majority of its empire in the 1820s. Just a few possessions, like Cuba, Puerto Rico and the Philippines, remained in Spanish hands until the end of the nineteenth century.
The dominant native cultures did the same thing to get that land before the Europeans arrived. The Aztecs colonized and subjugated plenty of groups.