You're the "Old World" now.
It's basically been ~~350~~ 250 (edit: correction) years now since US independence, and a decent while now at being a global power (~100-150 years?). These are timelines akin to that from the European Renaissance to the US Revolution (~1400-1800) and the UK emerging from the 1500s to being the "super power" in the war of independence.
Now, with the world's oldest constitution, and probably, depending on who you talk to, an increasingly critical mass of antiquated ideals and systems, the Presidency is more like the Monarchs of past revolutions than what remains of those monarchies, and the US's ideals and cultural influence something which most would rather move on and upgrade from.
Generally, I'd say it's one of the weirder and subtler historical events happening right now: the dissolving of the old lines between the "old" and "new" worlds. For me personally, this was once made clear when visiting Hannover, Germany, and its tourist attraction, the "New Town Hall", where someone who lives in British Columbia, Canada pointed out the similarities with their Parliament Building. The thing is though that the Canadian building is about 15 years older (both being just over 100 years old). Colonialism is long enough ago and Europe (and likely any other "old" culture, such as China) rebuilt enough and recently enough, that like X-genners and Millennials, the whole "young, hip, cool rebel" thing just doesn't mean anything anymore.