Wild arm flailing is a natural thing to do. Rather than condoning or condemning it, why not teach people to modify it.
Put your arms out to the side, palms down, arms straight, with your hands just slightly below shoulder height.
Now, keeping your palms down, bend your arms almost to a right angle.
So now, your upper arms are almost horizontal, and are sticking out sideways, and your forearms are horizontal, but pointing almost forwards, and your palms are down.
Now relax a little.
Your forearms and hands are very heavy, and you have now raised that weight to almost shoulder height, and have deployed it so that it can quickly be moved forwards, backwards, or sideways.
To throw the weight forwards, just push the hands forwards. to throw the weight backwards, straighten both armsor bull the elbows back (but don’t do both!). To throw the weight sideways, straighten one arm and, if necessary, move the other hand to a few inches in front of your chest.
The described position (arms out, bent at the elbows, palms down) is a sort of ‘on guard’ position which gives you a good starting position for useful and ‘structured’ arm waving. Start with the arms in this position, and return to this position when the ‘balance crisis’ has passed.
Honestly, it works, and it’s something I do deliberately when, say, practising riding one footed, or riding across rough ground when I’m on a uni with no handle.
A simpler way of describing the position would be to put your arms where they would be half way through a push up, but with the hands in the palm down position.