I think the key takeaway from this is that culture is self-selecting. If you are responsible for a growing company, culture will dictate whether you are able to attract and retain the best people for the job.
as for the actual point of the article, it seems highly inefficient to post problems and assume the right (interested) people will take them on. The obvious problems with this is scaling, and how do you account for people not working on the things that they were supposed to be doing. Basically, it's only something tenable in very few situations and only when a company is at a certain size. It wouldn't work today, for the most obvious reason that Google has a lot of kitchens!
[0] http://thefw.com/take-a-peek-inside-googles-internal-meme-ge...
This is an edict from the design team, which engineering brainstorming cannot overcome. Furthermore, the majority of engineers cannot implement a solution even if they cared to try: they lack permission to access the development Android source repository.
Maybe it's different in other product areas, but from where I sit, the atmosphere you describe feels like a myth that Googlers tell each other, and not part of its culture today.
I no longer work at Google but for the nearly 7 years I was there while not every complaint got handled by a group of engineers like described in the article, a startling number of them were. It was still very much a part of the culture when I left and I would not be surprised to discover that it still was.
The question is: Is it more or less efficient than alternatives, such as the fairly common practice of picking a software engineer out of a creatively-named-or-architected-hat and saying "You, you do it"?
If your selection process doesn't account for interest, you're losing significant efficiency on interest mis-fit. Nobody procrastinates harder than a software engineer with an ill-fitting problem.
I imagine an ideal scenario would be something between just letting everyone do whatever they want and having some tasks assigned, as there might be things that nobody wants to do but obviously still need to be done.
The right balance probably depends on the size of the company as well. For example I believe Valve is famous for not managing its employees and letting them work on whatever they want. I suppose they can only really do that because they are a private company though.