Simple transitive verbs can be associated with easily identified semantic roles. In the active voice, the subject typically identifies an actor or an agent, although other roles like observer are also available. Similarly, the direct object of an active voice verb is typically a patient or a theme, again alongside other possibilities that do not seem very difficult to discover.
These semantic roles are convenient labels. We can discuss clause structure, saying things like: "In this active-voice clause, the subject represents an agent and the direct object represents a theme. In the passive-voice equivalent, that same theme is represented by the subject and the agent is represented (if at all) by a prepositional phrase".
It's not a complicated system. It's also typical of transitive verbs to express an action, and these semantic roles describe how those other constituents relate to the action.
So, what do we do when there is no action? What kind of semantic role does the subject of "He is a student" play?
The grammar poses no trouble, and neither do the semantics of the clause as a whole. "He" is the subject, "is" is the copula, and "a student" is the complement. The clause establishes that the subject and its complement share their referent in the present tense. We can go so far as to claim that the copula expresses a state of being in the same way that a transitive verb might express an action.
But, what is "he", given that he isn't doing anything? "He" must have a role to play in the clause. There is no chance that the "he" of "he is a student" is as semantically empty as the "it" of "it is raining".
I cannot and will not accept that there is no such role. I certainly can and would accept that there is no general consensus. In fact, I'd find a lack of consensus unsurprising and unremarkable. All I want is at least one viable contender, one reasonable description of how the subject of a copular clause behaves semantically, independent of the grammatical relationship that attaches it to its verb and independent of the denotation and use of personal pronouns.