The USA maintains military bases in all corners of the world. From Australia to Guam, Eastern Europe to Brazil. If they're not interested in hegemony and all they want is to spread democracy (sounds eerily similar to the jesuits in the 1500's trying to christen the savages) why would they do that?
If US is able to spread democracy all around the world, it will not be the "Hegemony of the US". It will be the "Hegemony of Democracy".
Consider Germany after WW2. Allied won over Germany but did US establish a "US Hegemony" in Germany? No. They established Democracy in Germany. Once you give people the freedom to self-govern, you can not have hegemony over them, unless you are a corrupt state. But assuming that US is a working democracy, corruption will be rooted out, because people will vote for its removal.
If you want a more recent example Iraq was crushed, but not put under the US’s boot. It may have failed nation building in Afghanistan, but it tried rather than adding more territory.
Right, only authoritarian governments are interested in conquering territory.
Russia is trying its best to annex Ukraine to itself. But it is not "Russia" that is doing it, it is the authoritarian government of Russia. When did US last annex territories?
The workhorse of authoritarian politics is tribalism. They try to say it is a competition between countries and or races and or religions. They get supporters by making them believe it is their tribe against other tribes that is threatening their very existence.
But the real fight is not between countries or "tribes". It is between Democracy and Autocracy, and that fight is happening in every country.
