All I know about this is my own experience, but the photo below is my own OTTB’s race record, which is arguably more aggressive towards the end than Kochees, as hers were actual races and not just 4F workouts.
She didn’t break down.
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Edited in case the screenshot isn’t readable: Raced 2/22, 2/15, 2/8, 2/2, 1/21, 1/12, 1/4, 12/22, 12/14, 12/4 [short break switching tracks], 10/11, 10/2, 9/18, 9/10, 9/3, 8/25, 8/18, 8/7, 7/31, 7/24, 7/16, 7/8, 6/17, 6/11, 6/5… etc etc.
47 races under her belt. Most of those were a mile, give or take a bit.