Trust,
granted it is easier to understand your way but either way makes sense.
If I say “it cant be night and day too” that means it cant be both at the same time. OF course it can be night and then day afterwards. “You cant have your cake and eat it too” MEans you have to choose one or the other you can a) have your cake (i.e have it in your possesion) or b. eat your cake. You simply cannot do both at the same time it is one or the other.
Interestingly some poeple do say “You cant eat your cake and have it too” but thta is less common and (according to one account)actually helped lead to the arrest of the unabomber.
Wikipedia has an entry on this idiom that includes early versions going back to the 16th century