I’ve spent a lot of time at the end on these topics, to reply to some of your questions:
1- generally this cannot be done. The coverage of the pregnancy in semi-private is normally “activated” 9 months after the subscription of the insurance. You may find some exceptions, but that is what I’ve seen in most cases.
2- I don’t know
3- I think you are more or less right in your estimation
What I think is important in my opinion, more than the “privacy” which is more personal, is:
general better care (faster, more attention dedicated to the patient). You normally have much shorter waiting times for the exams, you can more easily get a second opinion, people will often treat you differently if you have semi, and even more if you have full private. Of course in Switzerland standard health care already works very well, but still when you have serious sickness these things matters. You also cover yourself in case the health care quality will progressively decline, as it is happening in many countries.
free choice of doctors
These things are not so easily attainable with just the mindset of upgrading from general ward if something happens.
Given that these advantages are less “clear” than the simple semi private or private room, you need to carefully choose your insurance provider:
not every provider will offer you the same speed of treatment
you need to pick a reliable one, that hopefully will be there in 30-50 years, when you will not be accepted by others.
cheap providers when you are young may not be when you are old.
difference between Flex and semi private varies a lot. In some companies like Swica the treatment with Flex is the same as for the semi private, in most others the treatment is better with semi private.
Keep also in mind that the important points that I mentioned above are sold together with many other less important aspects. For example, if you look at Helsana Semi Private (which is a good insurance), some important things (fast track, second opinion) are mixed with many others (balneotherapy, nanny service, household service, travel costs) which are much less important and that of course you pay for.
When you compare insurances you also need to see how the premium will change with age (it will). You need to expect at least ~70k CHF spent in premiums over a lifetime with a flex, easily more with semi-private and I think even 200k CHF or more with private.
It is very difficult to estimate this number correctly.
I went at the end with Swica Flex Semi Private, which in my calculations is one of the cheapest ones over a lifetime and a well known Swiss insurer. This is of course valid now estimating the premiums at old age, everything can change, but with the current information that seemed the best for me.
Imho not worth.
Wife canceled her semi private before 2nd birth and we paid ±800chf for 4 nights in Zollikeberg Spital to get single room. We asked for it, but know people get lucky if hospital is not full. Also I think that if hospital is full you might not get private room even with semi private. Aren’t with natural birth sometimes you are let go home same day? Don’t ask, had two c-cuts.
What else semi private would give that your OBGYN could participate in birth if all planned. We had two premature/urgent birth thus in that moment you don’t think about choosing doctors or that your OBGYN come with and just go with the flow. But in two different hospital we got very good care, both with and without semi private.
Not sure if there are other benefits. Better food maybe (or not from generic canteen)? But once you hold your small fresh “potato”, you don’t care about the food or room that much, until it covers your basic needs But private room is nice, especially if wife needs more time to recover. But hey, maybe your potato would meet another just born tomato and make friend for life in non single room?
In general I struggle to see benefits for semi private. Option to be able to choose doctors?
In emergency I guess you don’t care. In prolonged treatment ie cancer or planned heart operations (tfu tfu tfu) to choose better hospital/doctor? But you kneed to have some insight into topic then. Otherwise it’s just lottery that because of your semi private you will get more senior doctor assigned by random? No clue.
I recently thought hard about it, I think the main benefit for me it to hedge against the degradation of health services seen in nearby countries (from what I can see in e.g. France / UK, but I assume elsewhere as well).
As others say I don’t really care much about private room, etc. (esp. given that more and more things are ambulatory anyway).
But if things slowly degrade and specialist appointments start taking ages even for fairly serious issues, that a huge benefit (and I don’t think I’ll easily be able to get supplementary later).
(There is still a huge risk of sunken cost fallacy, but I estimated my lifetime cost and it might be a luxury I’m able to pay so currently decided to continue paying it, even if it’s really expensive – the premiums get fairly high quickly with age, tho mine is plateauing at around 40 or 45, which is much better than many other offers)
Question: since it is not a compulsory insurance, can the insurance company « kick you out » unilaterally? If for whatever reason they deem one is too expensive I guess nothing prevents them from doing so (contractually speaking).
Can my insurer cancel my supplementary health insurance if I make a claim?
Nearly all insurers state in their terms and conditions that they will not make use of this option, although by law both parties to a contract have the right to terminate it. The general policy conditions are decisive. Policyholders can always cancel after a claim, as long as they do so by the date of settlement.
Back to this - actually I’ve only seen 365 days being explicitly mentioned with some insurers (Helsana, CSS).
Others don’t really list it explicitly - is there some sort of general rule (that everybody seems to hide )?
Not really, afaik they could only cancel after having processed the claim.
Not that uncommon e.g. for legal insurance, if they realize that they will not make money in the future with you (because they believe future claims clearly outweigh the insurance premium).
IMO, that makes sense for voluntary insurance of non-essential things. But for healthcare it seems wrong (& for basic insurance also not allowed).
The whole discourse toward young or healthy people is “you should buy supplementary insurance now because you may not be able to later on, when you need it, if your health deteriorates”. That discourse goes belly up if they start kicking people out after 1 major claim or recurring need for treatments, which is what most people are afraid of (although there is also a comfort part to the supplementary insurance).
Insurers have an incentive not to make it a known habit of kicking people out after a serious claim because that would destroy their business model of attracting healthy people. That being said, they can and they may. Insurance companies really are warded against their clients (it hits both ways, as it also allows clients to cancel their insurance without regards for the silly 5 years delay after signing it that many policies have but while I agree for it for most insurances, I don’t think healthcare should follow this model).
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But private room is nice, especially if wife needs more time to recover. But hey, maybe your potato would meet another just born tomato and make friend for life in non single room? 
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