Why doesn't my processor have built-in BigInt support?

Question

As far as I understood it, BigInts are usually implemented in most programming languages as arrays containing digits, where, eg.: when adding two of them, each digit is added on

Answer 1

There are so many instructions and functionalities jockeying for area on a CPU chip that in the end those that are used more often/deemed more useful will push out those that aren't. The instructions necessary for implementing BigInt functionality are there and the math is straight-forward.