Short answer: Nope, and here's to death of the work ethic along with all authority! :D
Long answer: First of all, you're pointing to several things as the "driving force" of work: work ethic, profit motive, and authority/governance. I find the way you conflate them is unworkable (no pun intended), so I'll rework the terms in a somewhat different framework than yours, but I'm glad you introduced all of these elements because they are interesting and interrelated.
Also, to be forthright, I'm personally not interested in anarchy from the perspective of pros and cons, whether or not it will work, or is a reasonable alternative way of doing things maybe someday after we get enough people or something. To me, anarchy is not reasonable, is not a future or a society or a cause. It is something that people do--or a way of people doing things--which is inherently in conflict with the existent/dominant system (as well as a debatable span of other past and possible systems) and that I like.
The work ethic is a part of that system. It's a morality in which many people believe in the unimpeachable goodness of work (to put it very simply... of course it is more nuanced than that). It's interesting to consider why people have this work ethic. You suggest people have it because of authority/governance, and I think that's part of it. Government institutions do have a significant ability to make people believe these kinds of things; people who believed these things founded the US government and still continue to run it, and Americans seem to believe in this bullshit more than the rest of the people in the world. I think another reason people believe in it is pure stupidity.
The profit motive can't be what motivates people to work, since workers don't profit. Workers get paid a wage; profit is something else, and the fact that profit is systematically produced--and must be--is related to the fact that most people have to work for a wage. It is what motivates the system--and the people who own and run things--to run such that gain is the primary, or sole, interest. So in a way the profit motive is involved in motivating people to work. Or at least shaping what work is. Work wouldn't be what it is if it wasn't for profit motive. But this profit motive isn't as simple as "humans being greedy." Some humans may be greedy, others might not.
One of the funny things about your question is that in the existent/dominant economic system, people do work generously, and not in a greedy way. If people worked in a greedy way, would they allow business owners to profit off of their labor? In fact, to go back to the beginning, we could call the work ethic the system of morality which tricks people into doing this. The work ethic and the profit motive work well together. The work ethic is one of the ways people are tricked into working for another's profit without even noticing this is what is going on, because they believe in work.
You also say that authority or governance is what motivates people to work. One could say this is what stands behind the moral system. It steps in to enforce things if people don't accept their roles and the moral system that largely creates it. In the workplace, people are partly motivated to work by the authority there--the manager or boss. Outside of the workplace, other forms of authority function in ways that enforce the system. The government makes, enforces and adjucates laws that are related to the functioning of the same system including the government itself.
But I've done work where I had no boss or authority figure, and not because I believe what the government tells me. And I've worked even though I have no work ethic. And I've worked even though I've had no chance of profit, just a wage. What motivated me to work? I needed (and need) money to survive because I live in a world that requires it (of nearly everyone), so from a certain perspective one could say that this force is the "bottom line" of the system.
I would destroy the driving forces that make people want to work, as well as this "bottom line" that forces me to have to work. Work isn't freedom, whether or not one submits to it willingly.
Anarchy doesn't rely on generosity nor on anything really. It appears to be something that springs up continually and anywhere (though not always or everywhere), the incessant "no" to government, the will to do and be wildly, that cannot be suppressed. There have certainly been many people who have directed much of their energy to anarchic tasks without a profit motive, work ethic, authority or even generosity.
P.S. In this I'm not calling anarchic activity "work" in order to keep terms distinct and because I think work has a logic that's wholly incompatible with anarchy, but it's also just a word. Anyway I'm definitely not seeing where the lack of profit motive becomes a flaw in anarchy; on the contrary, that's one of my favorite things about anarchy, lol!
[edited for italics]