As someone that has lived in Switzerland for a decent bit now (but am not Swiss), I'm not sure this system makes a strong case for direct democracy working. I don't think the standard of comparison should be a functioning government, but rather some estimation of outcomes without direct democracy, if that can even be estimated. It's definitely worked well in some instances, and can be seen as not having worked well in others (in popular hindsight). The country doesn't even score as highly on a Democracy Index as several others [1], not that this is necessarily meaningful or conclusive.

[1] https://en.wikipedia.org/wiki/Democracy_Index