" more strategic your role -should- be. "
"The problem is too many upper managers think their role should be tactical. "
So this is a little bit mythologizing and there's a couple problems with this perception:
1) Everything is operational, and operations require material leadership at every level, there is no escaping it. Meaning, that there's a very material 'hands-on' component to even in higher level leadership.
The constancy of major decisions can have greater consequences and there are many more moving pieces, so it's hard.
Putting out fires and dealing with these grinding can easily overwhelm leaders but that's the reality of it, always.
Execs should usually have a much broader perspective that can help and guide decisions making.
Obviously, too much micro detail can be a problem, but that should be addressed by leadership that is willing to just listen and react accordingly.
I've been overridden by 'bad executive fiat' o occasion ... but also made forays where I shouldn't have because I didn't have the bigger picture.
2) Strategy is the most overused concept in all of business. While it's an important function it's usually a collective pursuit, involves input from various places - and most importantly, depends on details, i.e. downward facing.
Was Steve Jobs a relaxed, high level person setting strategy? Letting the details be worked out?
Musk?
Ford?
Bezos?
Not really.
There's a thoughtless comment floating here that points to 'Executives Asking Bad Questions To Seem Important' which is mostly wrong. They're asking questions to become informed. Some details matter, some don't but informing execs with a material understanding of the situation is a fundamental aspect of organizational communication.
The Tom Hanks film Greyhound is a neat study in that (He's the captain of a US ship leading a convoy in the Atlantic in WW2 getting hunted by German UBoats) - it's fully real time, you see a commander in the hot seat, and tons of activity around him. It's kind of interesting to see how information is propagated up and down and at what details. Obviously they're not building products.
Strategy, in the end, if it's done well should seem fairly obvious, even boring.
We have such lofty expectations of the term, that we expect 'enlightened divination' out of it, but more often than not, the result of good strategy should be a product roadmap that takes into rational consideration the aspects of market dynamics.
I think that having some creative analysts in a staff position to help the CEO maintain a broad perspective and take into consideration the more interesting market trends we often associate with the word 'strategy' is probably enough.
In my experience, I believe that in any company ... there is probably enough collective insight in the organization to set an appropriate strategy, it could only communications could work effectively.
That said, good execs are rare, and employees that are able to wrap their heads around the challenges that upper management faces are just as rare.
Finally ... the over/under managing issue is a really hard one, there are so many factors there.