Seems to be a lot of talking past each other in this thread with mixing of scenario elements.
And while I agree with you completely, there is an argument to be made that a student pilot does need a medical when training for their private in an LSA. It's the way the regulation is worded:
c) Operations requiring either a medical certificate or U.S. driver's license.
(1) A person must hold and possess either a medical certificate issued under part 67 of this chapter or a U.S. driver's license when--
(i) Exercising the privileges of a student pilot certificate while seeking sport pilot privileges in a light-sport aircraft other than a glider or balloon;
(ii) Exercising the privileges of a sport pilot certificate in a light-sport aircraft other than a glider or balloon;
It strikes me as one of those unintended things that sometimes happen in the drafting process. And, unless one is enrolled in a 141 course, there's really no such regulatory animal as "seeking" or "working on" a particular certificate or rating. So I agree with you. But it can lead someone, especially someone overthinking the reg) to the conclusion that unless you are seeking sport privileges you need a third class.
Note that the same analysis results in --- if all you do is plan to solo and LSA but never get any certificate above student, you need a third class
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