You can get a very exaggerated sense of the effect of BB/saddle/CoG height by riding a super tall circus bike.
What happens is that all "body English" movements have to be very exaggerated and you can't throw the bike into a sudden turn as fast.
That said, the difference is material at the extremes, but we're talking about a half inch or so here relative to 30-40 inches between CoG and the pavement. So, yes it does make a difference, and a lower bike may be snappier in hard corners and slaloms and the overall handling will feel more precise, but the actual difference is going to be pretty small.
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