All Demigods should be Assasins AND Generals
I don't see any advantage to being an Assasin over a general. The Generals can build themselves to be like Assasins but the Assasins can never build themselves to be like Generals. I think the idols should be just another item choice that all Demigods have access to. That is the strategy of the game, do I buy minions or not, all should be able to do so IMO and I don't think it would change much, just provide more options.
Also all demigods would have Stats boost tree and Moral boost tree in their talent trees. They could choose weather or not they want to invest any points in either tree. I think this would give more options to Assasins and Generals also because Generals would now be able to focus on stats if going for a non minion build. Maybe a slight amount of balance tweaking would need to be invovled but honestly I'm not sure there would be, having played most the demis and building most of them without minions I'd say the Generals and Assasins play pretty identical anyway.