Which is a nice way to not really explain anything. I.e poor story.

Purely IMO of course.

But this theory has no answer to why the dragons have their own Akatosh who acts nothing like Alessia's Akatosh.

I just figure that if each mortal race can have their own interpretation of the dragon god, why can't the dragons themselves? I still don't see how the details of each Akatosh are relevant, though. The important part, for the purposes of Skyrim, is that Akatosh stopped being Alduin and then, after that, retroactively gave birth to him.

Then we don't know if Alessia has a connection to it. That's what I was arguing against.

Her connection is peripheral in that she, by virtue of inventing Akatosh in the first place, set the precedent of the Dragonborn and allowed for Skyrim's plot to happen at all. Aside from that, no, she's not really connected. Her ideas of what Akatosh means for man and elvenkind, or what his "personality" would have been when she made him up, is not really relevant. Just that people started believing in him at all.

So, to use a metaphor, she's only about as connected to the split as a carpenter's teacher's teacher's teacher is to a table. Connected, and in her own way vital, but not to the level of "oh, I'm glad Bob taught Bill so Bill could teach Jack so Jack could teach Jim so he could make my table."

She may have given Borhamu a method to fight against Alduin, however. Unless I misunderstood you, you were saying that Alessia invented Akatosh which caused Borhamu to form. There is no evidence for this.

The Dragon's use the word Akatosh so you know who they are talking about. For the same reason Argneir translates "Kaan" as "Kyne" for you.

I'm saying that the reason Alduin is not an undefeatable god is because that aspect was weakened by the creation of Akatosh when the timeline sewed back together because he was not only, in the "corrected" timeline, Akatosh's son but he also now had to compete for belief. Now instead of all humans worshipping him, it's just certain Nords.

So no, all I'm saying is that Alduin was changed into being defeatable by the creation of Akatosh. So yes, we did have a minor misunderstanding. Oops.

How did Alessia creat Akatosh, and why haven't others done the same?

By believing super hard. And the Selective had some help from a Tower.

You're simplifying things way too much. The Nedes in Cyrodiil worshiped a version of Auriel called Akatosh. Allessia made a compact with Akatosh to do the whole amulet of kings thing. Then much later, the Maruhkati trimmed the elvishness off of Akatosh and Akatosh retroactively became more aligned with men (though not enough to separate Auriel and Akatosh). This is when we get a full departure from the old Nordic pantheon and begin seeing Imperial Gods. Then Tiber Septim came along and the Cyrod's religion became the dominant faith of Men, displacing all others.