To me the “Fun fact” contrasting 訳 and 理由 is borderline inintelligible:
The reason that わけ may be used for 理由, but 理由 cannot always be used for わけ (especially at the beginning of sentences) is because わけ is another way of reading the kanji for 理由. However, the more common kanji for 訳 will never be read as りゆう.
I have zero idea why the fact that 理由 is a secondary spelling of わけ helps understand the nuance between the two.
I already complained about that in the past but I find that bunpro always taking the stance that meaning “comes from kanji” or that kanji comes first and the reading choice is a post-hoc decision is frankly a bit absurd and in this particular instance really confusing IMO. The word わけ came first, the choice of spelling is only relevant for the written language (and わけ is very often spelled in kana anyway).
All that to say that I after reading that paragraph I still have no understanding about when わけ should be use and when りゆう should be used, regardless of character choice. And I think that’s the really important part.
It just makes things more confusing because now I had to go back and hover every instance of 理由 in the preceding lesson to check the furigana and make sure that it was meant to be read りゆう and not わけ…