Elgard isn't even the main character of her game though.
The issue is that we don't know the extent to which Byleth affects the plot.
Avatar characters range from being literal silent nobodies like Mark to literal main characters like Corrin. The fact that the titular Three Houses are pushed so much lead me to believe Edelgard, Claude, and Dimitri will all be major characters at the very least, if not the Lyn/Eliwood/Hector to Byleth's Mark. In theory, though, they COULD be more akin to Xander, Ryoma, and Azura: major characters but not main lords.
Edelgard more than likely being a prepromote kinda falls into the latter, but the focus on Three Houses implies the former more so. Either way, considering we have only seen Byleth use swords so far, it's possible Sakurai could pass him up anyway in favor of Edelgard, who has become an early fan favorite among the Fire Emblem fanbase.