Once you have eaten the cake, it has been consumed and is unusable. "Have" in this context is to possess something in a usable state, ergo "you can't eat your cake and (still) have it too." I guess it kinda works the other way, but in reverse order it more conveys the idea that you can possess a cake in a usable state, however you cannot consume it if you do. What then is the point of owning a cake you can't eat?
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Your neurodiverse (Aspie) score: 91 of 200
Your neurotypical (non-autistic) score: 107 of 200
You seem to have both neurodiverse and neurotypical traits