Good question, there is no reason for the word American not to follow “white”, like it does for Black and Hispanic or for it to be left off of all of them.
“White” is a colour (although it’s not actually a skin colour).
“African” is a geographic term.
“Hispanic” is a language-based classification.
For the structure to be parallel; the choice of labels should be:
1. White, Black, or Brown Americans.
2. European, African, or Latin-American Americans (or S. American Americans, or Iberian-Americans — none of the alternatives are very satisfactory).
3. English-speaking Americans, English-speaking Americans whose ancestors spoke an African language, spoken south of the Sahara desert; or Spanish (and sometimes Portuguese) speaking Americans.