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A clue is hidden in here, for those who will see it. You wrote:

Less than a logic puzzle, it's an identity test. With Cadance, she does the ladybugs rhyme which makes a large degree of sense (Chyrsalis never knew it, and the very test was demonstrated in season 2); with the other princess, however... it's a cut away to arbitrary, no-stakes-given, vaguely-described testing of magical skill or something, which is A. difficult imagine as being useful for assessing identity and B. not exciting to read with no descriptions or investment and with no meaning to it. Personal knowledge test, as done with Cadance, would far better serve Twilight's aim in determining the lie, and be more interesting by showing what information, memories, &c. she thinks is personally, privately, even intimately -- not that kind, stop sniggering -- shared with the other princesses.