I wouldn't call the interview process at Google broken. While some of my coworkers are better than others, I've yet to encounter any that truly aren't at the top of our field. Whatever we're doing, however we may fail in other areas, the primary goal of interviewing--to find and hire highly qualified people--is something we're achieving.
Yes, we may be rejecting highly qualified people who would do well at Google, but interview poorly. As has been noted in the comments here and elsewhere[0] it's far better to reject a qualified candidate than accept an unqualified candidate. Though we'd all be happier with a higher true positive rate, we're not willing to accept a higher false positive rate to achieve that.
What we're not good at, and what we get lampooned for so frequently (e.g., this story) is that in our pursuit of minimizing our false positive rate, we come off as arrogant, sometimes condescending, and a number of procedural and legal problems exacerbate that appearance. I've interviewed people that were right on the threshold between "hire" and "no hire", and like Joel advises, I wrote down "no hire". I'd love to tell these people what would have swung my opinion and ask them apply again in a year, but I just can't: it's too dangerous.
As far as interactions with recruiters goes, I can't really speak to those issues, since my experience in the hiring process was atypical (though not at all distinct in the ways we've discussed here so far, e.g. being hired for a company and finding a position after an offer has been extended).
Now, to answer your question, I have never interviewed anyone for a specific position. Every single person I've interviewed has been for engineering as a whole. People get interviewed for specific job ladders (e.g. SWE, SRE, SET, etc.) but the specific teams/projects a person will work on is decided after they've accepted an offer, as I understand it (and experience it myself).
By the way, just to clarify because maybe it wasn't really clear, when I said broken I didn't mean at all that the interview process at Google fails at hiring good candidates, I just meant that sometimes it takes literally months and that's too long, and that often people in the meanwhile receive other offers. For many of them it's not possible to say no to another offer just because maybe they will get an offer from Google in two months (and career wise it's not serious to jump around and leave a place after two months unless the position is a lot better).
That's all, and I think it's cool that you interview that way. Maybe I've had a biased opinion given what happened to the people that I directly talked to. Thanks again for clarifying these points.
Note that we do expedite the process for people who receive competing offers; I had an offer from another company the day after my Google interview; I told my recruiter about it and she had me an offer from Google within a week.
I explained in another thread here[0] one of the biggest sources of discontent from people who interview here, in case you're curious.
Yes, we may be rejecting highly qualified people who would do well at Google, but interview poorly. As has been noted in the comments here and elsewhere[0] it's far better to reject a qualified candidate than accept an unqualified candidate. Though we'd all be happier with a higher true positive rate, we're not willing to accept a higher false positive rate to achieve that.
What we're not good at, and what we get lampooned for so frequently (e.g., this story) is that in our pursuit of minimizing our false positive rate, we come off as arrogant, sometimes condescending, and a number of procedural and legal problems exacerbate that appearance. I've interviewed people that were right on the threshold between "hire" and "no hire", and like Joel advises, I wrote down "no hire". I'd love to tell these people what would have swung my opinion and ask them apply again in a year, but I just can't: it's too dangerous.
As far as interactions with recruiters goes, I can't really speak to those issues, since my experience in the hiring process was atypical (though not at all distinct in the ways we've discussed here so far, e.g. being hired for a company and finding a position after an offer has been extended).
Now, to answer your question, I have never interviewed anyone for a specific position. Every single person I've interviewed has been for engineering as a whole. People get interviewed for specific job ladders (e.g. SWE, SRE, SET, etc.) but the specific teams/projects a person will work on is decided after they've accepted an offer, as I understand it (and experience it myself).
[0] http://www.joelonsoftware.com/articles/fog0000000073.html