It would probably be good for Battle Mage to not get Staff of the Magus since the battle mage will most likely never use a staff as the main weapon.. seems like it just wastes a skill slot for them early on
No it doesn't. Everyone gets 3 Skills to start out with. Mages get a fourth skill: Staff of Magus. Battlemages get that one to give them flexibility - they can either go for melee or ranged magic, although they should probably also start with a staff as well as a sword.
Or at least be able to pick which of those weapons to start with (maybe they want to be a battlemage with a two-handed axe).
I mean, they keep saying "classless system", but then sticking us with very specific gear that fits (someone's) idea of a class.