No, it's not walkability that makes apartments in central Stockholm expensive. There's just not much more space there for more houses. For decades car traffic was what was prioritised. Just look at old Slussen which was just a couple of big traffic circles, with narrow tunnels for pedestrians. Or Sergel's torg, arguably the most central square in Sweden, which is dominated by a big traffic circle and with shops and pedestrian areas underground.

Then it is true that too little housing is built, and with the current very low interest rates people can afford to pay a lot for their dwellings. But I don't think it is intentional to not build more.