For most grad students in the sciences, their doctoral advisor has an extraordinary level of power over their professional and personal life. This is long overdue for an overhaul. No single person should have that much power over another, particularly in academia where institutions chronically overlook and enable misconduct.
Regardless of what the rules might say, the advisor levies day-to-day expectations and essentially has sole authority to rate the quality of student progress. Many advisors do this job well, but the number who are inadequate or malicious is way too high. This linear power structure can facilitate exploitation and abuse, but also provides a lower quality training experience. Grad students gain more when they become an expert while training in a diverse program.
There are so many ways we can repair doctoral programs. Here are a few:
In many cases, the major advisor is the primary (or sole) arbiter of the quantity and quality of student work. However, this represents a massive conflict of interest, because advisor is often the beneficiary of student labor, as it’s become a new custom to include them as senior authors on work published by the student. One way to fix this is to have the student’s dissertation committee chaired by someone who isn’t the PhD advisor. In some fields and countries, this apparently is the norm. I can’t tell you how many MS and PhD students I’ve talked to, who have been fully ready to graduate but were being held back by their advisor who wanted to extract additional labor from their student.
Admissions decisions in my field are primarily based on the decisions of individual faculty members, built on students networking with them before the application phase. (You’ll hear more about this later from me but for now) maybe it’s a good idea to think about letting actual departments and diverse committees do recruiting and selection of students? If the doctoral program is about student training rather than providing labor for PIs, then why is it so important for PIs pick their own minions?
For many doctoral student, the primary evaluator of the student is also their employer — they are often funded by grants that are run by the PI. If you’re not familiar with the way that grants are operated, the PI essentially has full discretion over the allocation of funds, hiring authority, and can make all kinds of capricious decisions without having accountability. If a student working on their dissertation depends on this PI for their actual paycheck, then this clearly creates an environment for exploitation sans accountability. I can’t tell you how many students I’ve talked to who have been harassed or assaulted by the PI of their projects who is also their advisor, and have been afraid to report because of fear of retaliation, or who got shoved out of grad school as a result of retaliation. Of course universities could benefit from having more transparency in how grants are run, but also, we can make sure that trainees have funding streams that are separate from the people who are responsible for deciding their professional outcomes. Students with TAships and fellowships are less susceptible to this kind of exploitation, but the power structures often put them at risk, too.
Not all research environments are required to have a program to train new researchers. If your institution doesn’t want to train doctoral students, they don’t have to! It’s not against the law. But if you actually are running a doctoral program, then this means the program should be there to support the professional development of the students, not just to use students as cheap labor in the research enterprise. This means giving them training opportunities and supervision across the program, from multiple areas. Yes, a dissertation is where you focus on a narrow question and become an expert under the tutelage of another expert, but we can do this without giving a single person so much control over trainees.
When talking about this previously, a few people have said to me that reducing the power of doctoral advisors would reduce their capacity to be highly effective. To that, I say: phooey, that doesn’t even make sense! The authority that a person has over another person doesn’t have to alter the impact of their mentorship. For example, I suspect some of the people who I have impacted most positively are people who I have had absolutely no authority on whatsoever. But I still funded them, guided them, enabled opportunities, and so on. If you can’t support a person to succeed in a diversified power structure, then how much are you really equipping them for the future?
Small Pond Science 
I forgot to post a link (again) to this critical chapter in the NASEM report: “Changing the Culture and Climate in Higher Education” that discusses the need for diffuse power structures and how to go about it. This is a well-researched and important piece of writing: https://www.nap.edu/read/24994/chapter/8
Change the funding model! If PIs do not need to spent months of work and energy and then wait for years with re-submissions to get projects funded, they would be less attached to their “baby” in general. A different funding model for grad students, away from PI grants would solve a lot of this. Students with personal grants have full freedom and all block/training grants I know (IGERT now NRT) admit on committee decisions and leave full freedom to students to pick advisers.
Research at this level is apprenticeship more than training. As such in some field at least adviser and apprentice spent a lot of time together, including in the field, in stressful situation as everybody is overtired. As such it is appropriate that not only the student gets to pick an adviser but also the adviser the advisee.
None of this is to minimize the abuses that exist, but there is more to the story…
I also agree that small committees (adviser plus 2 faculty from the same unit) with full decision power is an aberration, especially in the US system. Many other countries have different rules with outside evaluators (France) or external “opponents” (Sweden). This is a true issue, which needs to change, although some of these other models have their flaws too. “Advising by committee” is also challenging as you cannot get 3 faculty to completely agree on anything and this can be a mess for the student.
It’s at least as much cultural as funding-motivated. Mathematics doctoral students in the US are rarely funded by an advisor’s grant, but no other professor would dare tell someone what to do with their students.
Speaking for myself, my grad students aren’t cheap labor for me.* Most of them have pursued projects unrelated to the core of my own research program, which is supported mostly by summer undergrad assistants. But yet I’d be very opposed to letting my department or university centrally recruit grad students on my behalf, for two reasons.
First, I doubt they’d be able to recruit any students who’d want to work in my lab, because mine isn’t a traditional ecology lab. My core research program isn’t field based, doesn’t involve any charismatic organisms, and lacks direct conservation/management applications. So my lab lacks all the attributes that tend to attract most prospective ecology grad students. My grad students tend to be the rare ones who are attracted to ecology at least in part for other, atypical reasons (as I was back when I was a prospective grad student). My grad students also tend to like (or at least don’t mind) doing their own projects in a lab in which no one else is working on a closely-related project, which is another respect in which they’re somewhat unusual. A centralized, department- or university-based recruiting effort would fail to match my lab up to the rare prospective grad students who would like working with me. Which would mean I wouldn’t have any grad students. And no, I don’t think there’s some massive pool of prospective ecology grad students out there who would love working with me, and whom I’m failing to discover via my own recruiting efforts, but who would be discovered by a centralized department- or university-based recruiting system. This isn’t to claim that my own recruiting efforts are perfect, because they’re not! I’m sure there are some prospective ecology grad students who might well have been happy in my lab, but who never even heard about it. It’s merely to deny that a centralized department- or university-based recruiting program would be as good or better as my own recruiting efforts at matching up students to my lab.
Second, the training a grad student gets in my lab (or any good lab) relies on them being into their project, and getting along with me. Not because they’re cheap labor for me, but because they’re not working for me at all. They’re pursuing an independent project, under my mentorship and guidance. Perhaps I’m misunderstanding (and apologies if I am), but it sounds like your vision for grad school is that it should be reformed to be like an undergrad program? I.e. a bunch of faculty collectively imparting (mostly) non-personally-tailored training to a bunch of students? Because that way, each individual faculty member will have less power to affect the fate of any individual grad student?
*One reason, but not the only one or even the most important one, is that they’re paid by a combination of TAships, other departmental support, and their own scholarships/fellowships for 8 months of the year. I’m typically only paying summer salary from my grant. Further, my grant isn’t for a specific research project, so I can pay grad students to work on whatever it is they’re working on. In these respects, my lab is a pretty typical (or at least, non-atypical) Canadian ecology lab.