A couple of American politicians were executed in their homes a few months ago and one of the two presidential candidates was nearly JFKd in front of hundreds of cameras last year. A few years ago, a mob stormed the capital and erected a gallows to hang the sitting vice president if they could lay hands on him.
That’s violent enough even if you don’t consider the fact that de facto martial law is about to descend on major cities all over the country in the next few weeks. I’m doubtful that Greeks were anywhere near as volatile or violent as Americans are today.
What you're describing are anomalies. Most Presidental candidates are not "nearly JFK'd" nor do mobs storm the Capitol with regularity. For all of its cultural pretensions of being a nation of armed patriots always ready to "water the tree of liberty with the blood of tyrants" the US political system is for the most part incredibly stable and nonviolent. In ancient Greece, meanwhile, violent mobs, assassinations and tyranny were the norm rather than the exception.