This idiom confused me for the longest time, because I use “have” and “eat” very interchangeably. “Are you going to have dinner?” etc. I didn’t see that, rather, they meant “have” as a synonym for “keep”.

And yeah, it’s definitely backwards. “Have” doesn’t suggest “will have”, it’s a present term only. I have a cake, can I eat it? Yes. Switching the order makes more sense. Furthermore, I think “keep” at least suggests long term.

I propose “You can’t eat your cake and keep it too”

Yet still, who ever eats a whole cake? I definitely keep some for later.