I guess the problem is that the demigods don't actually wield items, they wield what they spawn with so to speak. Some items just straight up don't fit. Helmets for regulus, weapons for the rook, and so on. I agree that it would be a nice addition, but I fear it should have been added earlier in the production cycle of the game to allow for it to happen.
Overall, it is my sentiment and I think many others share this, that actually customizing your demigods would be a great feature. It may not be possible, but that is nevertheless my feelings about it.