The toddler scenario is a bit of an extreme circumstance. The last time that happened here was a 19 year old knocking a food canister over, and I think there was booze involved...
Yep, it's an extreme example, but it came to mind because it happened to a friend of mine, so I know that accidents like this do happen. Could have easily picked a different serious crisis like a holiday feeder dumping it's entire contents or something toxic getting spilled into the tank. Or my own experience - the time I used cheap root tabs that sent my nitrites sky high for ages, which needed 75% daily changes, using Prime and manually combing the sand to remove every tiny ball, and levels still rose dangerously high between 75% daily changes.
I just used my friends situation because it's simple, can easily happen and I genuinely wonder what @itiwhetu would recommend in a scenario like that, if large water changes are out of the question.
Most of us "water chasers" (I haven't heard that term before!) would do large water changes while manually removing/gravel vaccing up as much of the muck as possible, and it would likely require either the fish to be moved to clean water (effectively a 100% water change) or several back to back huge water changes to handle all that ammonia. Changing 30% then leaving it to the next day would just result in dead fish, so how can they say that we should never be recommending large changes? The emergency section of the forum is busy, and where many new and one-off members post their scenarios like this, and where the advice to do huge water changes is most likely to be given, so if they say that advice is bad and stupid, then I want to hear what they believe we should be saying instead. Ideally, backed with research and evidence.