"Why?" It's self evident in the bolded.
Sometimes the most important thing is the simplest.
The poor white person with cystic fibrosis will have:
race privilege
wealth oppression
health oppression
Each of these things matters in their own lane, sometimes those lanes are big and overlap.
The rich black person in hollywood will have
race oppression
wealth privilege
Someone arguing that the entire frame is bad because it essentializes, while then endorsing a more essentialized version to arrive to a more comfortable-to-Marla position

It's a nonsense argument, either you accept the terms of privilege and oppression or you don't. If you do, you are obliged to intersectionally compartmentalize. If you don't, you must come up with an economic model that prices these things. As a napkin example I priced race oppression as being worth $600,000 purely on a jobs/earning avenue. Obviously there's more oppression than that. You could also price it to something like votes, what someone's vote "should" equal given the weight of their oppression. An even harder task.
But instead of essentializing to a dollar amount, as that's going to disturb us and Marla, before she does exactly that, we can just acknowledge harms done in each category and address them more directly.
The rest is the usual "both sides are equally bad" nonsense that is a backdoor endorsement of the Republicans. No, most politicians are not billionaires. No, they are not equally bad. No, they didn't introduce the idea of stopping racism as the method to divide us. People trying to stop the stopping of racism are doing that on their own, and most of them are.. well, saying it like Marla.
Being a billionaire doesn't exempt you from racism, but it does give you incredible privilege. The existence of one doesn't negate the other.
Obviously. Indeed that's the attempted argument in Marla's post: but you can be white and poor and sick. But being rich doesn't negate racism nor prevents disability as well.
Marla's trying to have it both ways in multiple forms. The existence of privilege negates the oppression she cares about (shocking, the one that befits her identity), but the oppression of the other doesn't negate the privileges she doesn't want brought to attention (again, that befit her). To get there she complains about essentialization, but then essentializes the essentialization further to lead the reader to her inconsistent conclusion (where her preferred privileges and oppressions outweigh the others). You could argue scale (billionaire), and I would agree that being a billionaire is an incredible privilege. But I wouldn't essentialize it to one final score to exemplify why we should do away with all the uncomfortable categories of not-money.