No upper management. And no board. Now that is a scary thought. How would companies run without people in charge? We need someone there don't we?
Well, the Swedish approach was to look at the individual job responsibilities of the CEO, and determine if all of those functions could readily be absorbed by other people or bodies within the company (where they weren't already overlapping - and sometimes conflicting - anyway). So if you want to go ahead and do the systematic hard work, there's nothing that prevents you from figuring out which positions could (or should) be eliminated, with their responsibilities reallocated to other staff.
Of course, it's waaaaay easier to just go the observational humor route and declare "Hey, everything is so much better in the office when the boss is away, amiright? Let's get rid of 'em all!" So, kudos for that contribution.
More seriously, I see a couple of obvious gaps that you would need to fill, right off the top. For one, you need to develop some mechanism for larger-scale strategic direction. In the Swedish company discussed, that role was filled by the company's board of directors. For another, you need to have some sort of framework for handling civil and criminal liability issues when someone eventually screws up. Where does the buck stop, ethically and legally?