Main reason is that supposedly Akatosh (whoever he may be: I don't think he is simply someone Alessia created) gives the right of being a Dragonborn, not Lorkhan. Graybeards said so and the Dragonborn Emperors were aligned with Akatosh, not with Shezzar/Lorkhan/Shor.
Yeah, Alduin is supposed to be an Incarnate of Akatosh as well but... he is supposed to be an Incarnate of Akatosh only as the World Eater, not all the time (I don't think an Aedra can appear without an Incarnate and only while the Incarnate fulfills the Aedra's will are they the same person). When Akatosh decides that Time needs to end, he will send Alduin to do it (strongly supported by the fact that you did not devour his soul) and as someone who fulfills will of Akatosh, he will be Akatosh Incarnate. But until than, he is not and Akatosh needs to send another Incarnate to put Alduin to his place.
Alternately, MK once said that two personalities of Akatosh could fight at the same time. While MK's words are not canon, the conflicts in Skyrim could be interpreted as Akatosh having conflicting thoughts about something:
- Akatosh rules over world and it is materialized as Alduin ruling over mortals. He sometimes thinks about "Should I stop ruling with an Iron Fist?" and mortal resistance strengthens. The heroes that resist are his Incarnates of that thought and gods helping the mortals (by giving them Shouts) can be interpreted as the other Divines telling Akatosh to loosen the grip. Alduin's resistance is the Incarnate of the other thought: continue to rule myself
- Akatosh decides to loosen the grip for some time: Alduin kicked into the future with an Elder Scroll
- time to review the situation and decide if the world should end or if he should strenghten his grip again. Return of slavery and destruction of the world Incarnate as Return of Alduin while his "Should I let it stay as it is?" thought incarnates as the Dovahkiin
- he decides that mortal world is alright and Alduin is defeated. However, Alduin not dying shows that he still intends to destroy the world and Alduin will than return as the World Eater one day
OK, now start shredding the theories apart