I think you bring up several good points. In summary, it seems like you are saying that while elite schools do look for "interesting" people, they put parameters on the scope of interesting (in terms of admissions) based on their preference. I agree with this, and I personally believe that this is their right (and perhaps obligation), but I think the parameters are not as narrow as you seem to believe based on your examples. Furthermore, I think that this is a relatively minor issue since these are statistically edge cases or corner cases (most of which actually have a favorable disposition towards the applicant).
> Aaron Swartz
Admissions committees LOVE applicants like Aaron Swartz. Note that he enrolled at Stanford despite dropping out of school after 9th grade or so. He also had a lot of support from powerful people both at MIT and Harvard. He is an Ivy dream applicant.
That said, my understanding of the biggest problem that Aaron had was that: 1) he was breaking the law, 2) he was caught, told he was breaking the law, and was asked not to do it again, and 3) he did it again. This is why MIT went after him and why some of his support dried up (or at least became more subtle).
Large institutions with very public profiles have a right to draw the line at illegal activities that happen under their names or on their property -- some would say an obligation. On a personal level, I have found that many places are ok with gray area stuff, but blatantly illegal activity even after being warned is typically a no-go.
> vocal polarized opinions
I think this group is largely sought after. It's tough to say without specific examples. Let me try a few.
First, I have heard that one of the Beastie Boys (Mike D?) was accepted to Harvard in the 90s. The Beasties were extremely politically incorrect in a very PC time. This acceptance would not surprise me.
Second (a made up example), let's say a person of Sudanese descent supported female circumcision and wanted to advocate for this position. Depending on how their stance was presented, I think that this person could get in. If they said something like "this practice is important to me for xyz reasons, and i would like to go to [elite school] to help me learn about [specific topics] that will help me communicate my message in a more compelling manner", then that's probably a strong application. If they say something like "This practice is important to me, and I think all people in my culture should be forced to do it" is probably not a strong application. So there is a range of possible outcomes even on controversial topics. I think the key points are that the applicant needs to be curious about learning (esp. something that the specific school can help with), and the attitudes should probably be based on something of perceived high moral ground (law, human rights, etc.) rather than an individual's personal beliefs that may come across as being arbitrary. It can be a fine line.
A third (real) example is an applicant to a HYPS grad school who was accepted against all odds and violated most of the "rules" that people think exist.
The person in question was a minority rights activist -- the stuff they did was super cool. That said, this person had bad grades and unbelievably bad standardized test scores, neither of which were explained (e.g., illness, personal protest, etc.). The recommendations all said that the person worked on cool stuff, but was decidedly not academically oriented. They also said that the applicant struggled to write clearly, and this was easy to confirm based on application essays that were tough to read and full of technical errors and questionable decisions on style (but were still fascinating once they were understood).
This person was accepted and offered the best minority scholarship we had -- full tuition and a very healthy stipend. The applicant ended up not matriculating.
I give this last story as an example of how far some admission committees will go to admit interesting people. Granted, had this person been white or Asian, the rules probably could not have been bent this far. That said, I assure you that the "limits" can actually be quite loose even for these groups... if they are interesting enough.
> multiple failures
Yeah, this might be a group that falls through the cracks, but I would also consider this group to collectively be a corner case -- there just aren't that many of them. That said, I would suggest that if someone truly tries and fails multiple times in high school, then maybe their process has major flaws (e.g., too ambitious, poorly structured, etc.), and this might actually signal a hard limit on their ability to get things done.
Even then, it wouldn't be a terrible application to reflect on these failures and point out that the target school has one or more things that might help address these points of failure.
I'm open to other ideas or examples in this area.
SUMMARY
I certainly hope that you get to sit on an admissions committee one day. I think that you will find that most applicants are not interesting and/or not qualified and are relatively easy to reject. The interesting candidates are easy to spot and typically are easy to accept. They toughest part is filling in the bottom 30% or so of the class -- there will be no truly good options.