That's the cost over 4 years. Most people will be able to get financial assistance to help pay for that and you easily manage to make 30k (or less with grants) in 4 years to pay for school. People making below 35k per year are going to pay practically zero taxes. You can work about 15 hours a week making $10 per or full time over the summer to pay for that.
There's no need to take on any debt.
People in the US make considerably more money than those in the EU and, generally pay less taxes so there's a lot more disposable income available. I think people here prefer to be able to just get what they can pay for rather than hope the government will let them pursue the education they want (there are aptitude tests and quotas in some EU countries).
It's not really better ir worse, it's just different.
Sure, if you're a brilliant young mind and can get into Harvard and qualify for assistance with your tuition, you're set for life, basically, in a way no EU university can match. But for the vast majority of the population, the outcomes are significantly better with the EU system.
Also note that the gigantic tuitions at US universities are actually a relatively recent phenomenon (and a similar thing happened in the UK). Even in the 50s and 60s, tuitions were much closer to the current EU norm.
Of course, there is some room between these extremes, especially for unpopular subjects where you hardly even get enough students to fill up a professor's time. And in those cases, you'll also see that EU systems will essentially accept anyone. Typically, for uncompetitive universities and subjects (majors), the only condition is to have passed (gotten at least 50%) for the local equivalent of the SATs - a very low bar.
Granted, none of the top universities in my country even makes it to the top 500 in the world, so maybe this isn't a completely fair comparison? Actually, it's expensive by some other EU country standards - public schools in France and Germany, including PSL (ranked 28th in the world) and TUM (ranked 22nd), are free for all EEA applicants, with some nominal yearly registration fees (amounting to $1k in total for a 4-year degree). A more expensive school, like ETH Zurich (rank 7 in the world), is $4500 total for a 4-year degree if you're a Swiss citizen or EEA citizen with a Swiss work permit; it's triple that for an international student.
So yeah, when we say "university is crazy expensive in the USA (and probably UK too)", we're actually talking about the $30-40k numbers you're looking at. $200k and so are almost inconceivable to us.