If I was that rich, yet so addicted to junk food, I'd at least get higher quality junk food. My patties would be made from organic beef, in buns that don't fall apart, with vegan cheese from that one brand that I found exactly once, can't remember the name of but really loved (I fucking love cheese, but that one kocked out any real cheese from the cowmpetition)...
The food would come in reusable containers with non-porous surfaces that are easy and efficient to clean, delivered fresh and hot, made to order and delivered by students (cheap labour) on bikes (saves gas money), generously tipped for their express service (to incentivise continued quality service).
It'd still be cheaper than a decent meal, still be a pig move, still just as greasy and unhealthy, but at least it wouldn't be so embarrassing. And if it really had to be McD's, I'd pay to have it packaged into those generic foam containers that don't make it super obvious and delivered by unbranded delivery drivers (like generic DoorDash, Uber Eats or something).