Well, the scholarly consensus is that Mogadishu was one of the Swahili cities from the birth of Swahili as a separate identity until about 1500. In the 1300s, people from important families of Mogadishu married into noteworthy families from Pate, Mombasa, Malindi, and Zanzibar. So, on the basis of cultural, commercial and familial relations, Mombasa was quite connected as part of the Swahili cultural sphere.

Also, I would dispute your assertion that Ajuuraan rule over Mogadishu began in 1250. I will agree that there are ethnic Somalis in the Shebelle watershed, approaching the city of Mogadishu by 1250.

However, the sources that I read say that direct Ajuuraan rule over Mogadishu doesn't start until after 1500.

1500 is a quite important date, because it is in the early 16th century that Portuguese fleets enter the Indian ocean and severely disrupt trade of the Swahili states, sacking many important sites. So, the early 16th century represents a strong break between the "classical" swahili political organization and the Portuguese and Omani periods of the 16th, 17th and 18th centuries.

Prior to the full development of gold trade through Sofala (around 1200), Mogadishu was probably the most important and influential of the Swahili ports. It was largely because of Kilwa Kisiwani's strategic location as an intermediate stop-over point between Sofala and the Red Sea/Persian Gulf that Kilwa became more wealthy and influential in the Swahili network.

Yes, you are right that Mogadishu was a very wealthy city in the 15th century. It was at a key junction in the trade network connecting East Africa with Arabia, the Persian gulf and India. And it was because it was at this junction point that figures like Zheng He and Ibn Battuta visited the city. So, I don't really consider it "just another Swahili city" as you say.