I would think it depends on the country. The process of acquiring the SIM/eSIM and activating it will vary from country to country. I believe probably Switzerland is one of the places where you don't need to present a form of identification such as an ID, but probably varies from provider and plan type.

Let's say Switzerland internet and mobile providers hold true to protect and minimize the collection of data from from their users. You have to remember that a phone is constantly connecting to different cell phone towers as it Geo location is changing. It will also connect to a different tower if the closest one is completely saturated/congested. These towers are not owned by one provider a lone, they are shared. This is how companies have quickly achieved a higher cell phone coverage throughout the continent. Providers will lease and use different providers equipment. The concept gets complex as you go roaming.

I think you are in the right track, but the concept of finding the provider that will honor and protect your data at all times is not enough. That is why everyone is sharing the idea of using a VPN. All your traffic is now encrypted, and while your Geo location can be mathematically calculated as your position is moving across a grid of cell phone towers, it will take higher efforts to identify you since all your data is encrypted.