Great, so we're on the same page that investigating Oxman's academic output was an effective tactic for BI. Now if we're just going to focus on the social impact, I guess it depends on what it is that you'd like to see "moved forward". The people behind the campaign against Gay, including right-wing activist Christopher Rufo, have been very open and explicit that this was about advancing their agenda and that plagiarism was a means to an end [1] so you'd have to be pretty credulous to pretend that this was initially about academic honesty.
Rufo and Ackman managed to shift the Overton window and have achieved their goals, for example, by getting mainstream press outlets like the NYT to publish "just asking questions" articles linking Gay's ousting with DEI. Given that this was the original motivation for this whole thing, from my point of view, BI did a great service in pushing back on this agenda, and looking at Oxman as an exemplar of a white academic (recent academic who became famous for her academic work, whatever) was the perfect way to do this.
[1] https://www.realclearpolitics.com/video/2024/01/04/msnbcs_al...