Unfortunately, no. Cash is effectively getting phased out in Sweden; these days, there are more physical shops denying cash than accepting it.

Trying to make either a deposit or a withdrawal of "large sums" (> ~1K USD equivalent is my understanding) cash at a bank will get serious scrutiny and may even result in funds being seized or frozen.

Things have changed really fast, too. Just 2 years ago I don't recall ever being in a store which didn't accept cash.

And yet, all solutions other than cash are from private banks, which have no obligations to take you as a customer.

Unfortunately it seems like Sweden is far from alone in being on this trajectory, they're just a little bit ahead in this sense.

I do think that there's a case to be made for permissionlessly operated cryptocurrency on a public ledger here.

I never understood why some shops/restaurants do not take cash. It's only a minor inconvenience having to deposit the cash in-person and you don't lose money on any transaction fee. Maybe to protect against theft? But still, using cash saves the seller 1-3% on that transaction.

Even that isn't a universally acceptable solution; most countries will take dollars as well as local currency in some shops, but by no means all. And if you're from a non-dollar country your chances of international acceptance are much lower.