It's not to that extent. I mean, I'm Greek/Italian, as you know. In Greece we have the famous Turkish coffee, which has now been renamed to Greek coffee for stupid nationalistic reasons (if they wanted to change it, they could name it Arabic coffee, since this way of making it comes from the sandy deserts). It's the one where the coffee powder still sits at the cup bottom. Traditional coffee shops, unadorned and boring, are a men-only business, where the older men gather and play backgammon and a card game called "prefa". The modern, Western-style cafés are popular, yes, but so are juice bars, beer bars and especially the so called cafeterias where coffee is only a part of a whole menu: you also get ice-creams, juices, smoothies, hot chocolate, waffles and other sweets, fruit pies, club sandwiches and Nescafé frappé. The cafeteria is the most popular kind of shop in Greece, because everyone can find something to his or her taste.
In Italy, yes, there are coffee bars everywhere, but they are mostly the non-sitting kind, where you briefly sit at a stool at the bar, sip your espresso with a cornetto (croissant) and grab a panino to take with you before rushing to work. Or they drink espresso in a restaurant, after a meal.
The sitting cafés are more of a French thing, but there, again, it's not only about coffee. You can even drink wine there.
I think that it's the Korean snobbishness about everything Western and in particular European, which has taken this to such extremes. I thought it was mostly in dramas, but reading about it, it seems to be a real thing too, as seen in my quote from an internet article.