But reality is a lot messier than that. There are many pressures that support the admission of "unqualified" students to grad school, including state funding per student, the need for warm bodies as TAs or RAs, or the desire to grow a program. There are more spots (at least in my STEM field) than truly qualified applicants. Students with good recommendations, great grades, and research experience are admitted immediately, often without the whole admissions committee seeing the file. This doesn't fill up our whole program.
There are two kinds of "unqualified" that we will consider admitting--students with mediocre to poor grades, but great research experiences/recommendations and students with mediocre grades from well regarded programs (students with mediocre grades from unknown programs are just not admitted). The first group are often students who had to work a lot in school, students with learning issues (like diagnosed or undiagnosed dyslexia), or students who had to learn English while undergrads in an English language program.
The second group is full of students who got into a good undergrad program and then coasted and directionless students. Some of these students will be late bloomers, and be wonderful grad students--that is the case for one of my collaborators. In this case, the student had pretty poor grades from a pretty good undergrad program (which was used as an excuse for admission). The poor grades were clearly due to lack of effort, since this student discovered true passion for the field in their senior year as an undergrad, and excelled in research as a grad student. Alas, this is generally the exception and not the rule. The result is a department full of mediocre, poorly motivated, and difficult students with a few gems that are heavily sought after.
A huge additional problem for faculty members is the quality of the BS degree (which is no fault of the students, to be sure). As GMP said,
Another issue is the complete devaluation of the BS degree. It's become almost what a high-school degree used to be 30 years ago. Now you can't do almost anything without a BS; also, in order for everyone to get a BS, it has become watered down, with emphasis on breadth rather than depth, so basically all in depth technical training is now deferred to grad school.
When I was a grad student, I and my fellow US-educated students noticed how far ahead technically the European and Asian students were than we were. We had all received good grades, and did well in our programs, but the emphasis on liberal arts meant there was a lot less time for core instruction in the details of our field. This is a mixed blessing--several of my European colleagues are jealous that they never got to take classes in history, literature, or art (which I thoroughly enjoyed myself). On the other hand, I lacked a lot of depth in my field. This causes a few problems down the line. First, incoming students must be treated as if they have limited technical knowledge and skills at best, which means lots of training for people running labs. Second, lots of people don't really know/understand what the field is really like, which leads to a relatively high attrition rate of people abandoning their programs after a year or two.
This devaluation of the BS degree means that the MS and PhD have followed suit. Since the BS students are coming in with less knowledge, more of the PhD has to be spent on bringing them up to speed and less on more advanced training. We also don't want PhD training to last more than 5 years or so. Given that a fair fraction of the admitted students are less qualified, and that we want to maintain the value of degrees in our department, we end up tailoring expectations and experiences of the PhD to the students' end goals. Otherwise, too many would not make it through.
Personally, I will not grant a PhD to anyone not capable of doing PhD-level technical work, but I can already see that some of my students will be better than others at things like writing (papers and proposals), idea generation, working independently and other scientific skills. The department has a line in the sand to get a degree, but in practice, this is worked out by the PhD committee. What are the requirements of a PhD scientist? How can we make uniform standards for people with uneven skills? As a committee member, it is really, really hard to see someone working hard who will not make it. Sometimes, it isn't apparent until the student has been around for a while. I am a replacement committee member for someone on the bubble (who had been in our program for 3-4 years), and it is really difficult.
And what about my standards? Should I not allow a brilliant researcher who writes poorly in English to graduate? What about someone who is wonderful at scholarship in general, but is weak at generating new research ideas? These people would be valuable assets in the right position, but will never be successful faculty members because they are good scientists, but not necessarily good scholars. They have PhD level training and PhD level skills in some aspects of science. Do we restrict PhDs only to people who are capable of TT-like positions? I don't think there is an easy answer.