Comment by zahllos

Further additions to your comment. Expanding on your downside: Big reforms like giving women the right to vote only took effect in 1971 on the federal level. On a cantonal level, Appenzell-Innerhoden had to be forced into it in the 90s by the Tribunal Federal, but well.

I'd add some advantages to the upside as well: some changes require a referendum, such as changes to the constitution. But there's more: a popular initiative can be launched and if you collect 100,000 signatures in 18 months, you can force a vote on your own law. This is most commonly done by political parties and adjacent organisations, so it is at least feasible that a privacy-conscious organisation could launch an initiative to make it illegal to store any kind of user-identifying data. It is even possible private citizens could do it. There would likely be a "contre-projet" arguing why this isn't a good idea, but there is often a for/against for any initiative or referendum and they get to present their views in detail (in paper booklets, the vote swiss app, and on the federal chancellery website).

Further upsides: unlike US/British/some other countries, nobody has a 50% voting block in the Swiss parliament and it has remained a coalition since the modern iteration of the country (since 1848).

Basically Swiss politics is extremely deliberative. I honestly think "we will quit Switzerland if they do this!" is a bit of a hyperbolic reaction.