Some people claim that referendums may lead to "wrong" outcomes, citing Brexit as an example. I think this claim misses the point of the Swiss system. The Swiss system is not just about getting "correct" outcomes through referendums; the very fact that people may force a referendum fundamentally changes the political system.
In a "usual" democracy, people usually vote for a party that is closest to their highest-priority ideological stance. For example, if your highest priority is tax reduction, you will probably vote for a party that promises tax reduction. You will do so even if you do not like most or all of the party members. This opens the door for politicians who are corrupt, or just not very smart, to get into the parliament, only because they represent a certain ideology that many voters support.
In contrast, in the Swiss system, you can promote your highest-priority ideological stances through popular initiatives: you just have to find 100,000 citizens with the same ideology, and then sign a petition that forces the government to put this issue to a referendum. As a result, when you vote for the parliament, you do not have to vote according to your ideology alone. You can vote for people whom you consider smarter or more honest, knowing that the ideological issues can be handled outside the parliament.
This means that, if a country switches to the Swiss system, the composition of the parliament would change substantially, with many incumbent parliament members losing their jobs. This explains why so many parliament members oppose the Swiss system. They make up all kinds of excuses (e.g. "Brexit"), but at the end, they just want to keep their jobs.
