I see your point and I think that brings us a bit closer to alignment. But I think if someone is __incapable__ of writing such a paper there would likely be many larger flags and they probably should not have been able to pass their undergraduate curriculum.
I do want to make it clear: I'm not opposed to arbitrary filters when there is a high number of applicants and you simply need to reduce the number. I am opposed to pretending that such a filter is not arbitrary. I think we need to be clear about how strong of a signal any filter is, and be quite explicit that they are not all equal indicators. That is my main point: being explicit about the strength of a signal.
On regards to training, I do agree that schooling isn't __just__ training, but I'd fully disagree that this isn't one of the most important aspects of it, even in grad school. Your first two years (in US systems) are nearly identical to a masters and highly focused on classes. What are classes but training? Even being a TA or lecturer is, in part, training (full instructor of record would not be). Post conditional, I still think you are in training at least up until candidacy. That is much more arguable given the variability of advisors, with some being very hands on (training) and some being very hands off (on your own).
I'd prefer something as "The purpose of PhD programs is to train people to advance the field." Because by all accounts, it seems like you've done this (even with the self-deprecating humor. That is exceptionally common in PhDs too lol). I still maintain training because this isn't the end, but the beginning. Post PhD is where you can choose to go to be an academic researcher or industry researcher (or abandon research). Those are the actual jobs (which should have continued training) but your degree is more akin to a certification from your institution. You do come out with a body of work that is distinct from the institution, but the institution's goal is not to keep you around and continue performing work. They are explicitly formed to graduate you. To educate you. And what is education except a form of training?
Fwiw, I think we are decently aligned, but sometimes text is hard to communicate, especially post by post. I do think your critiques are valid, even where I disagree.