First, one cannot generalize about "most people." There are over 7 billion people alive in the world right now, and it is impossible to ask most of them (approximately four billion) whether they are happy with who they are and their racial identities.
Instead, rather than trying to generalize about "most people", it makes more sense to compare Hurston with other African-American writers who have expressed opinions about their racial identity. Many writers such as Maya Angelou, Langston Hughes, and Alice Walker express admiration of the rich heritage of African Americans while at the same time acknowledging the reality of racism and oppression.
Authors such as Ralph Ellison, Richard Wright, and LeRoi Jones are more focused on racial injustice than Hurston and more concerned about the negative experience of being black in a society dominated by whites. The immediate critical response to Hurston's essay was mixed, with some critics appreciating the Hurston's celebration of her heritage and others feeling that it was overly assimilationist and exhibited an air of denial about the true sufferings of black people living in a racist society. Hurston's critique of people who considered themselves “tragically colored” offended some readers who felt that they had suffered greatly from racial injustice.
One particularly important issue is that Hurston's own childhood in the black town of Eatonville, Florida gave her an experience of blackness unlike that of many other African-Americans. Thus this essay seems somewhat more optimistic than that of many other African-American writers in terms of her attitude towards racial identity and somewhat uncharacteristic.