The MPD/DID thing could be a minefield but this an MCU project in full. No Netflix or Marvel TV type deal. So... I think we are wait and see with how delicate they will handle that aspect. Because I'm sorry but... Marve Studios LOVES it's humor. And there's lots of cheap "laughs" to be made off of the multiple personality side of the character, rightly or wrongly.
I hope I'm wrong about that.
As for whether this should be a part of Spector's character before his origin story in Egypt... That does make sense I suppose, and as noted above, makes something concrete that in the comics has been often hazy and negotiable by the various writers over the years. I definitely see where the best thing to do is to commit to one or the other for the audience's sake. Either he's dealing with mental issues and the Khonshu stuff is all in his head or in fact the mystical elements are real in universe. I totally get that would be setting distinct parameters for us watching to latch onto.
That said... I also understand that Moon Knight is a very off the beaten path type of character and property. His mental state, his connection to reality and his own "alters", the living multiple lives and us being thrown off balance in seeing his stories play out not knowing what's true or not... That could be done very well and make for a distinctive super hero show.