So, at the first selection round I disregard all travel insurances linked to credit cards, as they always require that a trip should be paid by that credit card for an insurance to be responsible. Which is kind of expected, but it is not what I want. I want to be flexible in payment methods, and if there is a 20 CHF discount for using a specific payment processor (a real example), being able to use it.
Then I narrowed on Axa and Zürich travel insurances. After comparing their conditions, I chose Zürich Relax Assistance, which is cheaper and seems to have a bit better conditions.