You are very right, in the sense that the text attached to the Fantasia suggests that there is a legend suggesting that drinking that special potion has a certain effect.
To be specific, the text says:
"Legend states that any who drinks this mysterious liquid before lying down for the evening will awaken a new man (or woman)"
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I had not seen the picture with the text before, so this is new information for me thank you.
Given this new information: it is clear that the Fantasia potions needs be kept rare to not break against the "Legend" status it currently has and I would definitely encourage SquareEnix to change the usage of the potion so that you have to wait until the ingame morning to see the change

.