Are all embassies required to issue ordinary passports?

No. According to the Swedish Passport Law, it is the government, or the authority decided by the government, that decides what - and to what extent - embassies issue passports and national ID cards.

Since a few years back, the Ministry of Foreign Affairs' position has been to concentrate the possibility of applying for Swedish passports/ID cards to fewer foreign authorities, especially in countries in relative proximity to Sweden.

You can always apply for an emergency passport at the Embassy - as well as at the consulates in Glasgow and Edinburgh - to travel to Sweden. You do not need to book an appointment for an emergency passport but be sure to visit during the opening hours for emergency passports (which differ from the reception's opening hours). The emergency passport is issued for you during your visit.

Opening hours for emergency passports can be found here.