Copyright requires an element of creativity and originality. The easiest code snippets for AI to reproduce are things like language syntax (loops, definitions, etc), implementations of common algorithms, and boilerplate, and an index would probably find a lot of matches for those, but are they original or creative?

Incidentally, answers on SO are licensed cc-by-sa, so it's easy to violate copyright when copying them; but no one seems to care, suggesting that small code snippets aren't an important copyright concern.

So the challenge for an index would be finding a rare case of creative, important code in a sea of trivial matches.