Of course the LSAT advantages the rich. Everything does. They have more resources to prep, more free time to prep in, and more access to people who know the LSAT is learnable.
That said, GPA definitely advantages the rich by more. Having less time to study because you are working a full time job while in school definitely hurts your GPA. So does being less likely to aim for grad school from the start of undergrad.
Prestige of institution advantages the rich yet more. Who do you think can pay for an Ivy League education protected from real grades by grade inflation without a big scholarship? How many poor kids even apply to one?
And if you think quality of work experience is somehow not beneficial to the rich with family ties to good jobs, you are kidding yourself.
So maybe it's the GRE that is so meritocratic. I'm sure the people who have been educated in private school or the richer school districts don't have any advantage on a test over the material that they were educated on.
Even in the laughable case that this were true and the GRE were more meritocratic, it is going to be pretty hard for a student to elevate him or herself past the other categories where he or she is disadvantaged by taking the GRE which can't provide any meaningful separation for top scorers.
So the GRE can help you get into Harvard if you already have a high GPA either as the result of advantages you were born to or because you beat the odds to get it. If you beat the odds and got a high GPA from a low income household you probably already can get a job that covers your expenses for however long you need to study for the LSAT anyway. On the other hand, if you want into Harvard without a great GPA possibly because you were working a full time job during college, good luck getting in with the GRE. It literally cannot distinguish you or give you an advantage over other applicants.
I'm not saying this because I'm bitter. My parents are highly educated, albeit not wealthy, and both in highschool and in college my highest priority was therefore always my studies.
I'm saying this because the LSAT is the most meritocratic part of Law School admissions. You know what score range you need to get into good schools. Depending on your natural talent at reading and reasoning it takes time intensively studying to reach that goal. If you are poor you may have less support and the goal may take an extra cycle to reach since you have to work more hours while studying. But the work has to be done. No prep class can ultimately change that. So if you are rich, privileged, and have been handed everything your whole life, it will take you nearly as many hours of study to reach your goal as a poorer person of equal ability who is already used to working hard.
If you want argue that the LSAT is a bad test of ability to be a lawyer. After all, they deliberately made a test for law school admissions which apparently is no better than the GRE at predicting law school success. But, don't pretend that the LSAT is being replaced by the GRE because it advantages the rich, when in fact the LSAT has been the best path most non-privledged people had into a place like Harvard Law.
If the GRE replaces the LSAT the best advantage the poor will be able to get is having an authentic personal statement about overcoming the slightly more insurmountable odds against them instead of the rich applicant's one about a purchased study abroad "helping" the destitute, poor, and disenfranchised.