I'm well aware of the history of US-Mexico relations, but no, it's not an equivalent. For one thing, there is not a multi-century history of attempts by US to fully occupy and annex Mexico (there were people advocating for this back during the Mexican-American War, but they were a minority even then, which is why it didn't happen). For another, Mexico is itself a colonizer state in all the territories which US took away from it. But, most importantly, last time there was an armed conflict between the two states was over century ago.
Well there's not a multi century history, because the US hadn't existed for multiple centuries, or even a century before it started going to war with everybody around it! We even went to war with Canada! Literally every single nation which has ever had power is a "colonizer state". Friggin Sweden and Norway used to be sprawling empires! You have "colonizer states" and you have "vassal states."
And this reality of the world remains true to this day. It's just that the means change. Alexander the Great wisely stabilized his massive empire largely by letting areas under his control maintain an exceptional degree of sovereignty, minimizing overt resistance to his control. The US took this to the next step by not even directly claiming nations, but instead simply remotely controlling the governments of these nations, and simply overthrowing/replacing them when they became uncontrollable - and repeating the process. Made even easier with democracy, which has a paradoxical tendency to elevate unpopular people on the take, rather than popular ideologues, to power.
Whenever there's any need - we can easily compel the various defacto vassal states under our control to act, even when directly against their own self interest. See: Germany for the most overt illustration of this. Extracting wealth from vassals became somewhat less relevant with the introduction of fiat currency. So long as we force the world to use our money, we can simply print money as needed, export the inflation to other countries, and it effectively functions as real growth - at least until the whole system inevitably collapses in on itself in a debt filled void.
