alt Hacker NewsBankID also doesn't have Windows support. There's a defunct app that used smart-cards but it's fully deprecated and does not function.
But yes, it's owned by the banks not the state; if anything though this increases its weakness.
You can use BankID to identify with the tax agency, the public health services and police. (and more: this is just what I'm aware of) and there's an expectation that you have a BankID.
Also to identify with the banks, which was the original purpose, and many other services. It's somewhat expensive to run an integration but many customers and other users have a feeling that it is especially trustworthy as a method of authentication. One use I've had is with a file storage platform, they have an integration so that one can create shares against 'personal number' through BankID, which our customers in the public sector really liked. No need for them to juggle some account, they just share a 'personal number' and we were good to go.
The main competitor is Freja+, or just Freja, or Freja eID. It's particularly popular among immigrants, as I understand it, though not as commonly supported, especially in the private sector. There is also a semi-public electronic ID, "Skatteverkets ID-kort", issued by the same company that produces swedish passports, which is owned by the french defense corporation Thales.