Even before Covid temporary requirements, many universities were dropping the use of standardized testing scores, like the SAT and ACT. The idea is "holistically" look at a student's application. To be perfectly honest, this was first used as a way to guarantee a diverse student body. It is true that poorer families, often minorities, did not have the means to compete with richer students.
Richer students could hire tutors for the tests. They had time to attend extra prep classes that working students did not have time for. The tests themselves had problems often around situations that were "normal" for richer students but outside the experiences of poorer students.
What could go wrong?
Well, it turns out that as the "holistic" view has progressed, the entrance criteria has subtly changed. In addition to social and economic hardship being considered, student activities counted a lot. Outside sports leagues, outside school volunteering, and grades, to name a few, are more important. And these activities are even more skewed towards richer households. A student without transportation means cannot participate in these activities as much. A family that does not have "extra" time cannot consistently get young people to activities and volunteering activities that make up much of the entrance decisions.
Poorer families might depend on students to work many hours, or spend time taking care of younger children or older family members. Poorer families often suffer with poor education options in elementary and high schools. Their ability to succeed is stunted.
I don't have an answer to this. Putting SAT scores back into decisions has the same problems it presented before. Using quotas based on race, wealth or circumstances is not legal, and they come with their own fairness issues.
I was lucky. My family wasn't particularly wealthy, but universities were cheap (about 10 times cheaper in the case of UCLA). Incomes are no where near keeping up with costs. And less expensive options in schools often lack the reputation necessary for the best jobs.
Equality of opportunities works in many nations. Free or inexpensive child care frees students to study and succeed. Health insurance does not wipe out income where health care is guaranteed.