I can see where a little bit of the frustration comes from here; there's a sense that by putting any person in the slot they are robbing the Karak of much-needed expertise in some other category. If the miner is selected for Stewardship, the halflings won't get their farms running properly, and so forth.
There are two defenses against this:
First, people don't sit around on their butts if not directly controlled. If the halflings aren't on the council as stewardship they're still going to grow plants, it will just be happening in a less organized manner with less Council control.
Second, if the Council wants to control it, then there's a system in place for that- the Stewardship advisor assigned a sub-organization with a lieutenant as its leader and then permanently dedicates a half-action to oversight, as per how our intel networks and the Watch worked in Stirland. This means that any advisor in any category can actually get at least some of the benefits and actions of all the other advisor picks.
So if Mathilde takes the Learning advisor slot it doesn't mean that Karak Eight Peaks will have a shitty engineering guild, it means that she'll need to make the engineering guild one of her overseen organizations in order to give Belegar reports on it and let him issue it orders. Likewise if she is in the Martial slot she'd better coordinate with the thanes because she doesn't have a lot of experience in ordering around conventional dwarf Throngs and seeing to their maintenance and operations.
If we don't want one of the Council slots, and want a more limited scope of responsibility, then this just flips around- essentially, we end up as the Council advisor's Julia character (referencing Stirland again). So if we want to oversee Karag Nar and trade but nothing else we choose the No Slot option and then approach the person chosen about that, if we want to go assassinating skaven we approach the internal martial advisor about setting us up with a Royal Assassin's Office, if we want to poke waystones we talk to the Learning Advisor about a waystone-poking budget and writ of authorization.
@BoneyM, am I generally on track here?