An index fund won't suddenly invest in unicorns or whatever else on a whim. They follow a particular plan (e.g. track a sector, track the S&P, whatever).

The members of an index fund are supposed to have little correlation; not the same goes for Alphabet's divisions.

Quite a few index funds comprise members that have very high correlation with each other, e.g. funds that track sector-specific indexes in health care, natural resources, etc.