I don't know how it's for native swedes, but last couple times I was visiting there (and that was a few years ago) I didn't even bother to exchange currency or have any swedish kronor in my wallet. You just can do everything without cash.
I live in Stockholm, Sweden, I don't think I've had cash in my wallet at any point this year.
Parking? Paid with an app (that charge my credit card).
Paying a friend or my kids for something? Done via the Swift app (instant bank to bank account transfer).
Buying veggies at the outdoor market? That guy will accept credit cards via a regular terminal or a phone with something like iZettle. Or perhaps even accept a Swift transfer to his phone.
Regular shopping, credit cards. At the corner tobacconist you may find an old and slow dialup-based terminal, but they are rare. Most terminals are online and operate at decent speed.
I'm sure there are cash-only businesses, but I'm not in the market for illegal drugs or no-receipt-handymans. :)