I think it's not just that but the fact that the country is literally packed. It's about 2/3 of my country's size,yet has 3 times more people. Haven't been to Switzerland but I can imagine most parks and other public spaces must feel quite full with people.
Switzerland is only the 13th most dense country in Europe. Notably, the UK and Germany are more dense.
You can easily double it, because neither Germany nor UK have mountains covering half of the country.
Similarly for Zurich, there are significant hills around and most flat space is already built up.