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[Philippus Flavius Homovallumus]

Congratulations, you have constructed a straw man.

"That Lady is Hot" has a litteral and a figurative meaning. "The die is cast" has two litteral meanings in English and one in Latin, it's also a classic crib litteral translation. Interpreting "The die is cast" has nothing to do with brainpower but common usage. Common usage leans very heavily towards the fixed fate meaning and away from the chance meaning. Further, there is nothing in the translation to indicate a bias.

I say again; the tradtional translation is unacceptably ambiguous and also somewhat awkward in modern English in its intended meaning.

So let's break this down.

Alea: noun definition, a gamble, game of chance, or a gambling piece.

In this case we can assume Ceasar means the latter because of the verb but he's refering to a gambling piece rather than any other sort of gaming piece so we translate it as die because that's a singular gambling piece.

There's a problem here though, die is hardly ever used today unless you need to explain the rules of a game of chance; many, including some here, don't even realise that die is the singluar because dice are usually paired when we use them. So we use the plural because although not litterally correct it immidately conveys what Ceasar is saying to a modern reader without changing the meaning. The number of dice is totally irrelevant to the remark. The action of throwing one or two dice is exactly the same in this instance, a gamble.

Iacta, from Iacto: verb definition: to throw, scatter; to shake, toss about: (mind) to disquiet: (ideas) to consider, discuss, mention; etc.

This is traditionally translated as "cast" which is again fairly litteral because "to cast" i.e. "to cast the runes" is an accurate rendering of what Caesar is saying.

To why have we chosen "Fly high"? The problem with "The die is cast/tossed/thrown/shaken", or even "The dice are tossed" which changes the meaning of the remark not at all because they aren't litteral dice, is that none of these convey in English that the dice have yet to land. That is the reason for the change, the current translation conveys Ceasar's acknowledgement that his gamble has yet to play out for good or ill. To make it clear that this is an event under way. Your own proposed translations indicate you suffer from this confusion, you have suggested "The die's been tossed" i.e. past tense, wrong tense.

So now we have "The dice fly high", why the "let"? to compensate for the shift in meaning, where previously we had a statement about an action perfomed now we have a statement about an event underway. By adding "let" you bring it back to Ceasar's original meaning by indicating the remark is linked to his actions and decisions and not just about fate.