I think the idea is that if you want to have such a large portion of your realm in a message group, then you might as well just talk to the whole realm.
There is a distinction between the Senate and the rest of the realm. The Senate is the ruling body.
But allow me to petition for an automatically generated council: "All Lord and Government Members". That would do the trick.
![Wink ;)](https://forum.battlemaster.org/Smileys/default/wink.gif)