Starfleet's rank system included the ranks of Lt. Commander and Commander. Only four navies on Earth use those ranks, the US, the UK, Ireland and Canada.
If Starfleet isn't model after the US, then which navy they
are modeled after is a short list.
The Federation President is actual elect by the Federation Janitorial Service, in a secret ballot down at the union hall.
China is the most populated country in the world, India is the second most populated country in the world. It's rather naive to think that a worldwide government could be implemented without them and a few others having some say in how it will function. In a democratic world the USA represent only a small fraction of the population. It's likely that they'll only contribute for a similar fraction in how the world will be administrated.
It's pandering to an audience but otherwise incredibly naive to think that the laws for example will be handled the American way.
Well, the United States did have an impact on political systems around the world as it is.
For instance, the use of the title "President" for the head of state of a sovereign republic was originally "invented" by the United States. Latin America soon followed that example in the early 19th century. France became the first non-American country to do the same in 1848 and eventually pretty much everybody else followed suit.
The First French Republic in its latter phase had still attempted to emulate Ancient Rome by appointing Consuls as its highest government officials, but when the Second Republic came to be in 1848 they dropped the bullshit and went full American, so to speak.
Nowadays both China and India have presidents too (although strictly speaking, the title the Chinese leader uses in their language could be translated as "chairman" just as easily... it was the deliberate choice of the Chinese government to translate it as "president" to follow international convention).