Thanks for the response thetownclownsa.
Good to know that I won't achieve much with Allianz.
I guess I am looking for more day-to-day assistance as an expat with weak language skills, e.g. understanding complex Swiss requirements, finding an English speaking doctor to register with, or even something as simple as knowing when the rubbish collection day is in my neighbourhood.
Both here and in the UK (where the Amex Platinum concierge is FAR superior), I never found their travel booking services particularly useful. In the UK the prices were often higher than could be obtained yourself. Here they are simply too lazy to research things properly, e.g. they wanted to book me into a hotel that was still under construction! Thankfully I had the sense to do a quick online search before I said yes. Naturally, there was no real explanation or apology for their mistake.
I see that cornercard Platinum use Quintessentially, although according to Quintessentially's website they don't operate in Switzerland. I wonder if anyone has any experience with Cornercard?