It is not a perfect or rigid system, but it's the one we have (and any attempt to improve it would get caught up in the weeds of how much 'racial science' can be endorsed by the US government).

Practically speaking, most Americans over the past 300 years knew of specific near ancestors who came from somewhere else (with little interbreeding among immigrant populations) and answered based on that. The obvious exceptions were descendants of slaves and Native Americans, which is why those were the first non-white (where 'white' includes all Europeans as well as large parts of the Middle East and North Africa) categories tracked by the census.