If there was a market for SAS routes to those countries mentioned, SAS would have been there. SAS does'nt fly low yield routes where the pax mix. is'nt right (e.g. too many holidaymakers).
However, Scandinavia is well served by airlines from the middle east region. Iran Air from Tehran, Syrianair from Damascus and Aleppo, Egypt Air from Cairo, Turkish from Istanbul and Ankara, PIA from Karachi, Lahore and Islamabad, Sri Lankan/Emirates from Dubai. Kuwait Airlines, Royal Jordanian and MEA used to fly to Copenhagen from Kuwait, Amman and Beirut.
In addition Maersk Air operates a code-share with SAS on routes from Copenhagen to Cairo, Istanbul, Athens and Venice.
SAS got rid of their big aircraft in the last part of the 80's (1987-1988-1989), when they got their new smaller B767's. I guess the reason was that they wanted smaller aircrafts which was better suited for Scandinavia. At one stage SAS philosophy was to offer mainly nonstop services from the destinations they served, and the B767 was very well suited for these operations.
SAS used to operate to destinations like Los Angeles, Nairobi, Johannesburg, Rio de Janeiro and Santiago de Chile when they had the B747/DC10.
Click for large version
Photo © Tim Williams