No, luckily our version is not tied to the SIM card at all and works on just wifi devices. It's also free for the consumer to use. For being a service primarily integrating with banks, i will say it works very well in Sweden and now most providers has started to support it. Sure, there can always be improvements and i wish there were a standard not owned by a company, but i'm also glad when my 80+ year old grandmother has something simple enough to authenticate that provides a reasonable layer of security.

If you are interested there's some details here https://sv.wikipedia.org/wiki/E-legitimation that lists the differences.