> And most people speak (or at least understand) English.
This is wrong. In cities where there's a lot of tourism, they might understand. Most Swiss people only speak their local languages (German or French). As for those living in Ticino, they tend to be better polyglots.
English is quite common to speak among Swiss from different cantons, since they usually stop caring about the other official languages after the compulsory school classes.
I find kind of ironic that I have better fluency between the official languages than many of my Swiss friends and work colleagues.
I met plenty of people in Lausanne who didn't speak English, or at least didn't want to speak English (it is hard to tell, and anyways, it doesn't really matter). I visited Montreal shortly after my 2 year stay in Lausanne ended and I was surprised on how multi-lingual people were there.
That doesn‘t match my experience.
About 40% of all Swiss inhabitants speak English at least once a week [1].
Anecdotally, I can't think of a single acquaintance younger than 50 years old that doesn't speak fluently. Everyone in Switzerland learns English at school for at least five years. Most even for seven years.
Some of my German speaking friends even talk in English to French speaking people, even when both have learned the other‘s respective language at school.
[1]: https://www.bfs.admin.ch/bfs/de/home/statistiken/bevoelkerun...