I think much of it had to do with the story they wanted to try to tell (One can debate the success of the story but I think it's clear of what they were trying to do). They seemed to want to tell the story of a person growing to understand some of nuances of the war and to grow as their own person from a result of those actions.

Yda herself presents some of the same problems some of the original Scions had with their character growth. Thancred, Y'shtola, Papalymo, and Urianger basically initially existed to be able to explain things that the Warrior of Light needs to know through exposition. The only time they could really grow is when they were put in a particular context where they're knowledge and hordes of resource really won't resolve a problem which is why Thancred, Y'shtola and Urianger worked so well in Shadowbringers when they were removed from the status quo and forced to adapt to a new situation.

I think the problem with Yda as the main figure of Stormblood is that this would not of put her far enough out of her status quo to make the conflicts Lyse has really work or they would have to be written drastically differently. Yda IS experienced, she IS aware of the complications of the war, and she knows particularly everyone involved in the conflict. There would be little reason for Yda to go with the WoL to Kugane given she likely would have been less rash in response to the situation nor would there be any questioning in Yda’s mind on her position in the Ala Mhigian Resistance where Lyse does express some hesitation from time to time.

Could of it been done? Yes, probably. Though it would probably need to be a very different story then what we got. Given Stormblood mostly seemed to exist to get the Ala Mhigo and Doma subplots resolved as quickly as possible, it probably made more sense at the time.