Plently of polar-oriented routes operate today:
ATL-NRT
DTW-HKG/ICN/NRT/PEK/PVG
EWR-BOM/HKG/NRT/PEK/PVG/SIN
JFK-HKG/ICN/NRT/SIN
ORD-HKG/ICN/NRT/PEK/PVG
I don't think a polar flight is inherently more expensive/difficult. The problem with some (namely EWR-SIN) is that they are ultra-long haul so there needs to be a sizeable premium demand in order to cover costs of overflying everything. SEA-DXB would be at least 1,500 miles shorter than EWR-SIN, though.
ATL-NRT
DTW-HKG/ICN/NRT/PEK/PVG
EWR-BOM/HKG/NRT/PEK/PVG/SIN
JFK-HKG/ICN/NRT/SIN
ORD-HKG/ICN/NRT/PEK/PVG
I don't think a polar flight is inherently more expensive/difficult. The problem with some (namely EWR-SIN) is that they are ultra-long haul so there needs to be a sizeable premium demand in order to cover costs of overflying everything. SEA-DXB would be at least 1,500 miles shorter than EWR-SIN, though.