I found myself wondering about this question, and thought I would ask… I suspect the answer people will use is “likely no, because it hasn’t been done.” But hear me out.
Here’s the more specific framing of the question: are there any race situations where it might be better to train a leg-dominated swim (sidestroke, combat sidestroke, something else involving fish or dolphin kicking, or even a streamlined continuous flutter kick), planning to give up (possibly a lot of) time on the swim over the faster front crawl*, but recoup that on the bike and run? I’m assuming a well-trained elite athlete here, not a weak-swimming AOS for whom the answer might be trivially, “yes, because they can’t swim front crawl”.
Pros:
~90% of the time in HIM and IM triathlons is leg-and-core-based endurance work (hip muscles are critical for run and bike so I include ‘core’). Why not make it ~100% and scrap the upper body muscular deadweight entirely? This would have clear racing benefits on the run, and on the bike leg for hilly courses where body weight matters. It would also have training benefits in that there would be synergy between all three disciplines rather than tension between swim and bike/run. Finally, some alternative leg-dominated strokes (e.g., the sidestroke) would easily allow fueling during the swim; others might too. We know the front crawl does not make for easy fueling.
Cons:
-lost time on the swim*
-legs possibly already tired going into T1
-drafting likely much harder if you’re not swimming front crawl along with the rest of the leading pack
*-this assumes that crawl is in fast the fastest open-water swimming technique for humans. This might be the case, but just because we haven’t found a faster technique (or one that is leg-dominated) doesn’t mean it doesn’t exist. Actually, competitive swimming has identified a faster ‘stroke’ for humans than the front crawl over short distances: the underwater fish kick and underwater dolphin kick – but I have not found any evidence that people can swim this long-distance/sustained over triathlon distances (breathing issues a likely barrier… though stroke regulations in competitive swimming also likely an issue; successive bouts of underwater dolphin kick might be faster than front crawl – is anyone aware of any triathletes who have swum this way?). Humans have not evolved for swimming prowess and swimming is not a natural motion, but other aquatic mammals with four legs and most fish swim primarily with power from the rear of their bodies using their biggest muscles.