How to address situtations where the effort to avoid plagiarism results in less effective communication?
Let's split this into two different cases:


Is re-using a speech self-plagiarism?
Is re-using a speech appropriate in that specific classroom context?


Addressing the first question, the reason why self-plagiarism is an issue is that there is an expectation of novelty in scientific communication: re-using text from a previous manuscript is thus "cheating."  There is no such expectation of novelty in speeches.  It is thus just fine to re-use content in a talk, and there is not even any requirement to acknowledge that one has given the same talk elsewhere.  Consider, for example, a person doing faculty interviews and giving the same talk at different places: this is perfectly normal, acceptable, and even desirable.  Now, if you give the same talk to the same audience multiple times, they'll probably get bored and stop inviting you to talk, because you don't have anything new to say.  Similarly, because talks are often tied to manuscripts, e.g., at conferences, it will necessarily be the case that they contain much new material.  Still, these are byproducts of the nature of the communication, not ethical principals.

Now, to the second question: should the student have re-used the same speech in class?  Here, I would say that it depends greatly on the educational goal of the class.  If the goal is to workshop particular aspects of the content or delivery of a speech, then I think that it would be fine, since you can work on new aspects of a speech even if it is not new (or even yours!): for example, you might want to work on delivery and oration, and even just quoting Martin Luther King could be just fine for that.  If, on the other hand, the goal is to learn how to create a speech, then it's failing to satisfy the educational objectives of the class.  To take the analogy: even if Martin Luther King's best speech was "I have a dream," it shouldn't mean it's the only speech he can ever give.  I wouldn't call it self-plagiarism, since novelty is not the default expectation in speeches, but it would be failing to follow instructions.  Not knowing the exact nature and instructions of your class, however, I'm not sure which category it falls into.