Fully agree, except it should be possible to use at least part of the minor's logistics network as well. IMO it would make sense that as the "major" partner, you'd be able to convince your vassal that it might be a good idea to let us use their country for supplying our armed forces.
Though both passage through territory, and logistics, through minors that are your vassals, should require some type of card to be played to allow this. Additionally, having your units and logistics clog up their country's networks (which although they don't actually affect the AI in the same way as we are affected, one would imagine that this would be the case) should have some kind of impact - ideally, it should be properly modelled such that this affects what gets shipped where, meaning it could lead to production shortages or food shortages and the like, which in turn could lead to unrest, which could lead to events triggering where your vassals asks you to help with their food shortage that you've created (then you could choose to supply them with temp food (further clogs up logistics), or just detour a brigade to help reduce the number of hungry people to a more manageable level ;) - with associated political/reputation consequences).
By default, it should definitely be possible to march your troops through your vassals territory without immediately have to declare war - though if you haven't played the right card yet then this should result in PP + rep penalties (and possibly trigger an event/report related).