I agree with you. A few do, many don't.
I think the economics are different in different countries.
In Germany, we have "Zuständigkeiten," but the English translation "responsibilties" contextually does not match the implicit meaning of the German word. It is in some ways closer to "Reviere": precincts.
In a typical large car dealership, there are basically procurement, salespeople, mechanics, management, marketing, and finance. Only the smaller dealerships (which are rather workshops), consisting of one, two or three people, are different. They usually have a good overview of the big picture, but not so in a large dealership.
There, everyone looks after their "turf" and tries to make the best of it. This structure simply doesn't allow you to take care of other things. The German paradigm of "productivity" ultimately means "as few people as possible for a clearly defined responsibility". It's all about control. And they are usually not enough to get their work done. If someone gets their work done, it is considered suspicious to be underutilized.
The consequence is that they concentrate precisely on their task, usually perform it reasonably well and usually very efficient, but have no time to look after a forum, for example. A paid "forum observer" is a no-go in Germany, something unproductive. There are very (very!) few companies that have a media officer or a person responsible for media matters. It's just not seen as something that contributes to productivity.
The old university teachings are still what make up the Bachelor or Master of Administration in Germany: they only count if they make money. And this is supposed to be directly measurable money, $/h/person.
PS: This "structure" (actually it is a problem) unfortunately applies to almost all companies in Germany (but of course not to the authorities. Unfortunately, they are not only unproductive, they also completely lack media competence).