I see this claim a lot, but it seems partially true at best. As per the article and conversations with friends in admissions departments, the testing requirement at many elite schools was suspended due to the coronavirus pandemic.
However, the debate over how tests impact disadvantaged students may be why "many schools continued their test-optional policies even as the public health crisis eased" as per the article, so you're partially right that it probably played a role in why some schools have dragged their feet. (Contrast to schools like MIT which also dropped their testing requirement during the pandemic but reinstated it more quickly afterwards.)
Still, I don't know anyone who works in higher ed admissions who wants to get rid of standardized testing for "restorative justice" reasons. Rigorous schools need to be able to ensure they don't admit students who have no hope of graduating and competitive schools need to winnow down the number of applications to a number that they can actually review.
My impression is that the objections to standardized testing typically come from groups outside universities like the NEA, FairTest, teachers unions, parents, activists, etc.