The rich also use more government infrastructure (think roads, their companies may have trucks and other vehicles). Their goods move on roads built and maintained by society.
The rich also travel more and internationally. That means they're going to use the TSA, FAA, Air Traffic Controllers (probably FAA), the State Department, the US Embassy, the SEC (or Treasury, not sure who governs currency exchanges), and host of other governmental services and regulations that that go along with inspecting airline companies and regulating them - that someone who does not engage in international travel would use.
Or for instance, a hedge fund manager needs the Securities and Exchange commision to protect them more than a factory worker. There are multiple examples like this where the rich use more government resources.
Housing? the 5 million households in America making more than $200,000 a year get a lot more housing aid than the 20 million households living on less than $20,000. It's not even close.
https://www.cbpp.org/research/housing/chart-book-federal-housing-spending-is-poorly-matched-to-need?fa=view&id=4067
Don't wanna get into a debate on who uses more government services. It's just really hard to quantify tbh and it'd be an exhausting debate.
But like I said, it's in the best interest of the super rich to keep the masses educated and heathy so they can keep purchasing goods and services. Not to mention having educated people working for them.