You miss Blooms point in my opinion. But of little consequence anyway.
I may be oversimplifying it (here I'll confess I've only skimmed through The Closing of the American Mind - just found too much of it a series of hackneyed right-wing talking points I didn't want to venture further) but an education centered around a defined (Western) canon was certainly one of his core arguments and I say the real threat to such an education today is the business-centric model of our institutions of supposedly higher learning, not the oft-mocked faction of diversity and intersectionality which still constitutes a relatively small part of our campus culture. Even the other Bloom, the redoubtable Harold, made a clearly more forceful case for the canon than Allan ever did despite being rather opposed politically.
Let me close by sharing some of my own college experience (think about 10 years ago). Like everyone else I had to take my share of required courses, and one of them was called Introduction to the Novel which didn't include a single book that I gather would've earned Bloom's (either one's) approval. (The closest ones were Richard Wright's Native Son and Alice Walker's The Color Purple.) But I can say the class discussions we had (at least the ones I attended) were often challenging and stimulating, including this particular one about Native Son that would've destroyed any idea of safe space when a white female student angrily protested that Bigger Thomas' decision to hide the body of the white woman he accidentally kills isn't excused by any element of structural racism, with no serious pushback on that uncomfortable truth from the rest of the class including African-American students. And get this: I found this other novel I read for (IIRC) a history course, a fine retelling of Romeo and Juliet called The River Between by Kenyan writer Ngũgĩ wa Thiong'o, more rewarding than either the better-known Native Son or The Color Purple, which BTW turns the very idea of the canon upside down, and the best conversation I had about the book happened to be with a Kenyan immigrant student... in a physics class (another required elective, yes). And I was also lucky to take another elective in ethnomusicology taught by a former Harvard professor who had firsthand training in Korean pansori (one time he began the class being introduced by a TA as a surprise "special guest" before coming out with a pair of Korean drums in full traditional hanbok) and which introduced me to the beauties of Indian raga music, a lifelong love that continues to this day.
All that was in my very first 2-3 semesters of college, no doubt the best part of my campus experience despite my general contempt for formal education. None of these examples would be considered part of the generally accepted canon, but I can say they were at the very least no less rewarding than the usual course work I did in European history, Aristotle, Palladio (architecture was among the first choices for my major, but I ditched it after taking the intro ARCH course - just way too time-consuming for me to make it a living), etc. And even while I was working on my eventual business degree (I believe you're an accountant yourself) I was doing my minor in philosophy with courses on logic, the obscure Medieval philosophers and Wittgenstein after taking, you guessed it, Philosophy 200 (or whatever the course number was) as one of my required electives. And that's not including the boatload of reading I did on the side - mainly the Russians including Tolstoy, Dostoevsky, Chekhov and, if I'm being honest, lesser writers like Mailer and Rimbaud - sometimes well into the morning in the dorm basement with nary a soul present, which really helped me get through many of the business courses which I found excruciatingly tedious (marketing was the worst).
But I digress. My point is that the kind of, yes, diverse intellectual environment that I found in my most rewarding time in college wouldn't have been possible had the Blooms of the world imposed their limited worldview on the college campus, and also that I was able to get my education DESPITE the coursework of my major which served as little more than a resume booster. To me the latter business requirements of corporate America are the real threat to our education today, not the supposedly closed mind of our universities where students can, pace the naysayers, readily partake in the (Western) canon and others' ideas regardless of one's origins or prejudices.