I also joined in 2011 (SWE, normal hiring process) and my experience has been nearly the opposite of yours.
I could have stayed a year and hoped for the best, but by then I suspect I would have been so embittered that I would have become the embodiment of a bad culture fit so I left before that happened because I had a great opportunity dropped right into my lap.
Now I suspect I am blacklisted at Google because a few people have tried to get me rehired now that such openings exist and they were immediately shut down by HR.
It's very easy at Google to transfer from niche to core. If we (in Search) see someone languishing in another part of the company with skills that we want and they want to work with us, we make the transfer happen, and there's nothing HR or another manager can do about it. It's much harder to transfer from core to niche, and it usually requires a solid track record of sustained performance in your original assignment. I know a number of people that transfer from Search to Google-X after 4-5 years, but I know of virtually nobody that can make that transfer after 1-2. (Basically, the company wants to "make back" their initial investment in you before they'll let you work on speculative projects that may not show a return.)
Arguably some of the niche projects would be better done as startups - they don't face the constraints of working at a large, very visible multinational where they don't get resources or attention from higher management - but the entrepreneurial spirit isn't quite dead at Google.
I also didn't know upfront that little tidbit that whatever assignment I took, I would be stuck there for 4-5 years. If I had known that, I would not have accepted my initial assignment, nor any other, until it was something I knew I'd remotely enjoy, and I'd probably still be there today.
So by relentlessly focusing on short-term ROI, Google lost 100% with me.
If they're going to insist on blind allocation, then they ought to not be surprised when it doesn't work out. But I gather the heuristic is to assume these cases are a 100% indicator of non-googliness.
For me, I was with you until I read your suggestion to "read your comments" to learn about your experience.
From my perspective, Google recruited me aggressively away from a long-term gig where I had an absolutely stellar reputation. I uprooted my career with the mistaken belief that they wouldn't do this unless they had a reasonably clear idea what to do with me. Apparently they didn't and I'm not the only one who had an experience like that.
Sure, I could have said no and I take full responsibility for saying yes and for everything that happened as a result of doing so. And once I realized that Google was going to be of zero help in fixing what I think was a minor allocation error, I once again took responsibility to do what it took to fix the problem myself: I left.
So here's why I think they wouldn't help: the team onto which I was placed was losing an engineer a month. Every time they got a noogler to say yes (3 times during my short stay), another team would intercept them before they got to their first day on the job. The work was dreadful and tedious and the manager even seemed to hate running the team. And the only reason I said yes was because I had this naive faith that Google wouldn't do something as seemingly daft as blind allocation unless they had a pretty good idea how to make it work. My bad. But not my problem. High level people should have been fixing the root cause here instead of continually throwing nooglers into the pit and expecting a miracle.