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I find proofs like this weird.

I can never quite understand what it means to say anything beyond:

"whichever of {a,b,c} is the smallest is the answer to both sides".

Who is this audience for which all this extra ink carries extra meaning? What additional insight can you have possibly communicated to them?

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One way of looking at it is training, you practise punching a bag and later you go box, you prove trivial results 5 ways then when you have a problem that isn't trivial you have 5 approaches in your locker.

It is a course exercise. The additional insight is that there are multiple ways to solve this exercise, one that most students would chose and another, explored in the article.

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