http://www.youtube.com/watch?v=JGfXiIXTpE0
More seriously, I think that allegedly financial calculation often ends up covering up for laziness, arrogance, and hierarchies of social class. Make sure the code works? That's QA's job. Make sure it runs well? Oh, that's ops; file a ticket. Wash my own dishes? Hey, office manager, get on that. Oh, and and honey, make me some coffee while you're at it.
I know some companies work that way, but I'd never want to work at one.
Testing is a little different: most professional software engineers consider testing an intrinsic part of software engineering, and so would never say, "that's QA's job". (But even then, there are some especially hairy testing problems that would benefit from a specialist's touch.)
Anyway, I think you're conflating dysfunctional organizations with specialization. In your example, developers say "that's operations' job" because they are lazy and don't care about maintaining a sane production environment. In a functional organization, they'll say the same thing, but they'll mean, "that's operations' job because they will do a better job than me". It sounds the same, but it means something entirely different.
(The same goes for washing dishes. I could wash my own dishes, but I would use a lot of water. If we batch up all the dishes in a 3000-person company each day and wash them in an industrial dishwasher, it will take less aggregate time and use much less water and energy. So while washing your own dishes may be symbolic of teamwork, it's actually a dumb thing to do.)
I know in my work, I've found that doing a variety of things, including "grunt work" leads many times to great works of creativity and discoveries of new ways to be more efficient. If you have a Ph.D. sweeping floors, you can bet they're going to take a stab at making the entire "floor sweeping" problem disappear. Not so much for a professional janitor.
Putting your head down and focusing is great when you have a mountain of obvious work to do. But that's not always what the business needs.
The high-end design firm IDEO specifically looks for "T-shaped people", by which they mean people who are deep in one area but have a broad set of skills outside their specialty. They believe that creative work is essentially collaborative, and that you can't be a great collaborator without a good understanding of what people are up to and the ability to step in and take a swing at anything that comes up, expert or not.
Another reason to avoid specialization comes, I'm told, from queuing theory. Unless your workload is perfectly regular, specialization leads to bottlenecking and global underutilization.
I'd also consider how Toyota, the world's #1 car company, looks at this. They do an immense amount of crosstraining, and line workers are specifically discouraged from specializing too much. Much of their efficiency comes from bottom-up innovation, which you don't get if people are focused only on their one little piece of the problem. (For more on this in particular, Toyota Kata is a great book.)
I drink 10-15 cups of whatever a day. The cups get tossed in the trash when empty, or left ..somewhere.. when I get an idea.
But stop me every time my cup is empty, make me break my train of thought and go fool with soap and water and a breakable cup? Likely the castle comes crashing down, and 40 minutes to rebuild it.
Might work for some, but definitely not for me. Wash your own cup; but leave me alone.
People are skilled economic resources, but they are also status-seeking monkeys that were mainly evolved for foraging, fucking, and fighting. If you don't keep that in mind when setting up an organization, there are risks. I'm asking how Valve handles them.
Regarding dishes, I'm not saying that one has to pick suboptimal solutions just for the sake of symbolism. Google, for example, has industrial dishwashers. But still, everybody picks up their trays, sorts the compost, recyclables, and landfill into proper bins, puts the utensils in the bins for used silverware, and then slots the tray and dishes into a conveyor that feeds into the kitchen. Could Google hire busboys? Sure. But they didn't, and I'd bet it's not an accident.
