While I understand that the phrase: “Où mets-je mes chaussures d'habitude ?” is technically correct for the exersise, I am having a hard time mentally processing when I would ever use first-person inversion. To me, it sounds incredibly snooty and stuck up and something I would never want to suggest that I am.
Is there a situation I would be inclined to use the first person inversion for asking a question, and why?
Indeed you are correct as some first-person subject and verb inversions can sound very pompous in French.
Take a look at the following Kwiziq lesson dealing with this very matter and highlighting some you may encounter -
Forming inverted questions in Le Présent, special cases: puis-je, ai-je, suis-je
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