Most of the friction I run into is related to the banks themselves - sometimes it's quite impossible to do business with them unless you have a Swedish bank card (or personal number). Examples of things I currently can't do without the above:
1. Refill my train/bus card online or buy train/bus tickets online
2. Use Swish, the Swedish half-answer between cash and cards. This is the bank-to-bank transfer protocol which is only supported by Swedish banks. It is quite convenient if you have it, you can enter in a 10-digit number which many storefronts display next to the register and it otherwise works very much like Apple Pay Cash (which is not supported here yet unfortunately)
3. Have a phone plan. I have to use prepaid and cannot top-up online. I have to always go buy top-up receipts from Pressbyrån
4. Buy from several various mom-and-pop shops that also only for some reason have card machines that support Swedish cards. They also always have a Swish number as mentioned above.
#2 and #4 are usually the most problematic. When I go out with people from Sweden and someone covers something I inevitably end up withdrawing cash as the path of least resistance.
#1 and #3 are related to a popular payment processor in Nordic countries known as DIBS, who currently likes to reject foreign cards but I suspect will eventually support them. I'm hoping Sweden's banks and other payment systems finish integrating with the rest of the world before eliminating cash entirely so as to not alienate outsiders.