South Korea has a load of infrastructure built up after SARS/MERS, no-one in Europe does, The option of "test/track all the people" is not on the table in Europe.
Heck the UK, who's response I gather you favour, are cutting the sets of people they test, not increasing them.
South Korea's success is all about their widespread testing.
The difference in mortality rate is because South Korea knows how many people have it, and Italy has no clue. Which, again, is because of testing, not quarantine.