It's true that the wording runs like that. But here's the angle: the Council is the body intended to represent the member states, so the member states are the ones who get to decide who is going to represent them in council. At the moment, that's usually the minister for the subject under discussion. It's true that on those occasions where it is the head of state, you probably can't get round sending your head of state (and probably wouldn't want to). But if a member state decides they are going to define their own rules such that it's an elected representative that gets sent the rest of the time, the rest of the EU shouldn't be able to overrule it, because that would defeat the purpose of the role being one that is under control of a member state.