Have can be a state of being verb. And a state of being verb is a linking verb. Why is have not a linking verb?
I have no reference to cite, just a bit of experience. In some languages, "have" indeed often expresses a state of being. However, in English, I have never seen it express a state of being. In English, we would say "I am hungry." In Dutch, "Ik heb honger" or "I have hunger." In English, "I am cold." In French, "J'ai froid" or "I have cold." Since we do not use "have" in the same way, as a state of being, then I am assuming that is why "have" can not be a linking verb.
'He has a degree in linguistics" vs. "he is a linguistics graduate" is a case where the phrases are interchangeable in speech or writing, but they are subtly different. "He has a degree in linguistics" would mean "he holds a degree" or "he has earned a degree." So, having the degree implies the action of holding the actual "paper" degree, whereas being the linguistics graduate is only about "being" the graduate.
"He has 2 legs" vs. "he is of 2 legs" is another very similar case of phrases that are interchangeable, but whose meaning is subtly different. Having two legs, means possessing those legs, a form of action. Being of two legs, is, again, a state of "being the creature" who possesses those legs. Hope this helps.