If "i.e." or "id est" is often used to say "that is...", why do we use "id" instead of "illud"? Doesn't "id est" translate to "it is"?
Translation between two languages is rarely as easy as swapping each word for its equivalent in the other language. Function words in particular, for example demonstratives like id and illud (and hoc, istud, etc.), don't align perfectly between English and Latin. Both 'it' and 'that' are reasonable translations of id, depending on context.
And in this instance, we are dealing with fixed expressions. It so happens that in English, the idiomatic expression is that is, while in Latin it's id est. This is quite arbitrary. The French expression c'est à dire translates literally to 'that/it is to say', while the Swedish det vill säga would be 'it wants to say' in English. It's perfectly possible to conceive of a world where English and Latin ended up with other standardised phrases than the ones we are used to.