Helping out with the grad admissions process at Maryland always makes me re-examine my department. This year, the theme to that re-examination seems to be the process of finding an advisor. At Maryland, for many people this process is self-directed. You think about what area you might want to do research in, take some classes, talk to some professors, and eventually ask one to be your advisor. I think part of the reason that some students have such trouble with this is that it's similar to asking someone out on a date - complete with all the anxiety that they'll say no, already have too many other dates, not want to commit to dating you for the next five years, etc. There are of course ways to ease into the advisor-advisee relationship (ways to have the first date without committing to marriage) - taking a class, doing an independent study, talking to them about their research, etc. Perhaps these can make the proposal less daunting, though I imagine that for the extremely shy, even doing these things is terrifying.
Still, I believe that this process is definitely better than the pre-arranged marriage. While the powers-that-be might assign you an advisor that you get along with and is in the area that you declared interest in when you entered grad school, you might instead end up with an advisor with a drastically different working style or change your mind about what you want to do. Even if you meet them once or twice before the marriage commences, it still bypasses the important courtship phase. Rushing the process does a disservice to all involved.