I think a different analogy might have made this work better. Frankly, an IT consultancy and a corporate environment are simply different sides of the same coin; both are businesses and one just happens to focus on helping others use technology (whereas, the "business" at which I work has education as a work product. Unfortunately, your analogy came across as a little arrogant (you know I like you, Erik! I struggled to find a good word in place of arrogant and, well, failed!).
I actually do quite a bit of consulting (and more all the time) on the side and also manage a small IT shop every day. As I perused your list of single day activities, I recognized the pattern and not just for me, but for my staff and many of my counterparts in small organizations - we all have to make major mind shifts throughout the day since we have few staff to support big stuff. Honestly, I think a lot of it is about breadth and depth in the organization. The more people you have and the larger you are, the more you can afford to keep skills sets narrow but deep. For smaller orgs, the portfolio is not that dissimilar from larger orgs, but there are fewer people, necessitating a broader skill set. Of course, the skills may not be as deep. Honestly, I think this is why some larger organizations have trouble bringing things together sometimes; many of the staff are so pigeonholed that it's tough to pull out of that and see the bigger picture.
The primary difference as I see it is the number of bosses and the level of engagement. When I do a consulting gig, I do my thing and get out. In my day job, I'm have to reap what I sow. I'm stuck with it. That's a very different support pattern and requires no less skill. It simply requires different skills. When I do consulting, I report to a different person for each gig.
I think I understand what you're trying to say but found the analogy a little off-putting. Yeah, I took it a bit personally

but mostly because I'm not sure it's 100% on target.
I sincerely hope my message isn't construed as an attack; it's certainly not!
Scott