I have no idea what is normal these days. Last night, I got into a conversation with Emmett MacFarlane about what to do to get into a Phd program. It was the result of someone asking folks with PhDs if they got rejected when they applied. I answered: yep. I distinctly remember two rejections, pretty sure there was a third, that a fourth school let me in without $ (which, to me, was tantamount to a reject--more below), a fifth that put me on their waiting list, and a sixth that gave me four years of funding. Which is where I went. The larger conversation was about whether students should contact potential advisors and whether places relied on individual profs making decisions about who they want to advise as a key part of admissions decisions.
First, some basics on Phd admissions. Don't go if you are not guaranteed funding for 4 or 5 years (whatever the norm is in your discipline/country). It is not just because going into debt is an incredibly bad idea for a degree that does not promise a job at the end. It is also that those places where you have to compete with those in your cohort for funding became awful places to work. It shapes the culture of the department, where colleagues are seen as rivals. Back in the day (early-mid 1990s), a few schools were known to be like this--Columbia and UCLA come to mind. I was lucky to be rejected by the former and, well, the latter was school #4 above. Everyone (the PhD students) was fully funded where I went to grad school, and, perhaps no accident (since we were trained to think of how institutions provide incentives), we had a great culture. People helped each other survive classes, we helped each other through the comprehensive exams, I received lots of useful feedback on my dissertation proposal, our practice job talks were most helpful, and, yes, we played a lot of sports and had more than a few drams of booze (Debbi Avant didn't teach us how to make cocktails--that came later). The more advanced grad students had time for the newbies. Grad school is not supposed to be fun, but, for me, it was some of the best years of my life.
Did I contact folks at UCSD and say, I want to do x, can you be my adviser? Nope. Indeed, I was assigned an adviser, did a heap of research for him in my first year on international telecommunications history (learned more about the Titanic than I would have expected). But I switched advisers when I started working on my proposal. And here's the thing, which is reason #1 I am not a fan of potential students matchmaking with supervisors before they start their Phd programs, my dissertation idea was very, very different from what I wrote in my application. Perhaps because US Phd programs essentially assume that you will start from scratch (compared to British ones where you have an MA and just do a few years of research, and Canadian ones that think they are the latter but are really the former--MAs are often required for admission but one still has to do two years of coursework, comps, etc), I have the view that the PhD program is not just for training how to do the research agenda that one enters with but to shape the imagination of what are interesting and feasible questions. I find it problematic that a student would enter grad school with an idea and then stay ruthlessly committed to that idea--I would hope that their views of what is a good question change. But that may just be my bias.
Ok, that's reason 1. Reason 2 is that profs move, die, change their minds about who they want to work with, are crappy advisers, or are actually truly awful people. So, a student commits to a place because they have the nod from one prof. What happens if that prof moves on? Or turns out to be incompatible? Or turns out to be a serial sexual harasser? Wait, am I saying that a department might let a serial sexual harasser select their next prey? The "individual profs give the nod rather than a graduate coordinator/committee" system allow for exactly that. Not that sexual harassment is as rife as movies depict, but it still happens and still derails students' careers.
Reason 3 for not having individual profs ok or not ok potential admittees based on their research compatibility has much to do with inequality. Who gets those precious admission slots? The profs that have the most influence? Influence and wisdom are not always correlated. The profs with the most money? Which makes sense in lab situations, but in normal poli sci situations? I am not so sure. Which students get the admissions? Those with the best connections to profs or those with the best ideas? Relying on the preferences of individual profs seems ... dangerous to me.
Reason 4: Applicant--undergrad students, MA students, and folks who have been out in the workplace--have really little clue of who is the appropriate adviser for them. Which then creates a lot of noise and work for profs who get random emails. Maybe if I had received more targeted emails over the years I would think this system makes sense. But maybe there is a selection effect--since my department does not select PhD students via individual profs saying who they will work with, the smart, strategic students know not to bother profs who can't influence their admissions? I don't know. All I do know is that I don't want to encourage more random emails.
There is, of course, survivor bias in all of this. That I was a happy accident. That my Phd students--most had topics completely unrelated to my own research agenda--have been mostly successful in this business. Perhaps I would have co-published with more students if they were in the same area as myself. The one student who did work closest to mine and used my work as a target was actually admitted before I arrived at McG. So, maybe my individual story shapes my preferences just a bit--that I learned a lot about other areas, other research agendas, rather than creating disciples or followers in my area of research. I see my job as helping students realize their own agendas, how to pursue their research questions as best as they can. I have Miles Kahler to thank for doing the same for me. I didn't do the "smart" thing at UCSD and do an international political economy project--which is what most of of the IR profs specialized in at the time. I followed my interests to wherever they led me--because I got into this business because I am a deeply curious person.