Maybe you got a "coordination number" instead of a "person number"? You only get the latter if you are expected to live in the country for longer than a year. The former "confuses" a lot of people and websites, which are not fully prepared to deal with it.

> Could you please elaborate or link to a resource on that?

Not sure what exactly you're looking for. There are 3 types of BankID: "on file", "on card" and "mobile". The first two are seldomly used and not all banks offer it (mine doesn't). I believe that most sites only support the mobile version. The mobile app cannot be sideloaded on iOS, and requires Google Play Services on Android. (For now it works on rooted phones. For now.)

Although technically minded people can still find a way to sideload the Android app without having to have a Google account, this is far from being mainstream. For most people you have to agree with Apple or Google's terms and have an account with them. If you're banned and lose access to the store, you can't install BankID any longer. It's not fun to live in Sweden and not have access to BankID.

I don't like the idea that you have to establish an asymmetrical relationship with a foreign conglomerate to be able to identify yourself in your own country and use digital services.

I think that having competition at least opens up the possibility that one of the players will introduce a mechanism that does not rely (solely) on Apple/Google technology. For example, a simple hardware token could work.

Regarding IDs for foreigners, I believe that the EU cracked down on Sweden and at least the government websites allow other European digital IDs nowadays. At least the option shows up in the list of authentication choices, but since I can't use that flow I cannot state how well it works in practice.