Would we say that a dentist's license had nothing to do with whether they can do dentistry and cheerfully go to one that doesn't have one?
Fact is that by getting the Ph. D., the guy did prove that he was "good" in some way; he had the academic "muscle" and that is relevant to the teaching, even if the subject isn't the same.
You absolutely cannot say that philosophy is irrelevant to literature. That is to say if we examine the statement "[w]e wrote again, pointing out that a Ph.D. in philosophy would prove little anyhow as to one's ability to teach literature" it doesn't really hold up. That fellow simply doesn't cast aside his philosophy background when he gets up in front of the literature class! The way we analyze literature all has philosophical underpinnings. Literature can carry philosphical points of view, and consciously so, even. Fictional literature has been used to transmit philosophical thought, from Socratic dialogues of ancient greece to works like the novels of Ayn Rand.
Since the school chose an instructor with a philosphy background, they asked that he have an objective certificate of high achievement in that respective field. That was arguably better than asking for a Ph. D. in literature.
I do not say that philosophy itself is irrelevant either to literature or the teaching of literature. I will say that there have been very competent philosophers whose judgment in literature is at least suspect--think of Kant quoting the poetry of Frederick the Great, generally regarded as pretty bad stuff--and that there have been very competent writers on literature whose grasp of philosophy isn't strong.
Shall I go home and remove from my shelves the criticism and poetry of T.S. Eliot, who never bothered to show up and defend his Ph.D. thesis at Harvard?
Picture a ven diagram where A overlaps with B, B overlaps with C, but AC does not overlap with A. Remove B and you have two circles that don't overlap at all.
Purge from your mind a whole aspect of who you are, and some other two parts become disconnected: uncontroversial to me.
Saying A relates to B and B relates to C says nothing about A relating to C.
Another tangent point to consider: dentists and other vocationalists have existed long before a licensing board did, and someone, somewhere, got the first History PhD.
In fact, I think this is a prime problem with healthcare in the US in the moment.
The problem James outlines is the same with professional fields: we assume that license X, which often requires degree A, is necessary for competence in an area, and that competence cannot be achieved in an area in any other way. As a result, we stop actually paying attention to competency per se, and focus on licensure, which is not the same. As a result of that, we lose choice: any other way of meeting a demand is assumed to be illegitimate and unsafe, which is untrue. Competition is lost, and monopoly is gained.
In your example, for instance, you suggest a hypothetical case where someone doesn't have a dental degree. But in reality, it's almost certainly not that that person would have no degree at all, and no experience, it's that they would have a different sort of degree, with a different sort of experience.
Dentists are maybe a poor example, because if anything, their profession is an example of one that is being stifled by current practice. I suspect that they are in a position to learn to do a lot more than they are, and are held back by professional licensing laws relative to MDs.
The appropriate example isn't "would you hire someone without a dental degree to treat your cavity?" It's "would you hire a dentist with appropriate surgical training to do jaw surgery?" Would you hire an optometrist with years of opthomological surgery training to do LASIK surgery? Would you hire a psychologist with pharmacology training to prescribe you lithium, or a psychologist with appropriate training to do TMS treatment of your depression? Would you trust your pharmacist to pick the right antibiotic for your infection, that has been precisely characterized by a lab already? What about a neuroscientist with clinical training to interpret your MRI scan?
Licenses, although well-intended, have become hindrances to lower cost and better choice. The tail is wagging the dog in professional fields exactly the way James suggested over a century ago.
The stakes in that case are rather higher. A literature teacher who screws up won't make your life anywhere near as miserable as a dentist who does likewise.