First: we both know how to use search engines, so your assumption that poor rural Americans use the most...etc could also stand to be backed up with research. But fair point, here's some proof for you:
I don't have access to academic papers, but here's the one they're referencing: https://www.nature.com/articles/s41560-020-0579-8 in this article: https://www.vox.com/energy-and-environment/2020/3/20/2118481...
1) The very rich use vastly more energy (much of it in travel, but also in the production of the stuff/properties/vehicles they buy) than the rest of us so that means they rely on the energy infrastructure more. Energy infrastructure uses all the logistics infrastructure (rails, roads, ocean, air, pipelines, etc).
2) Higher energy use means they have a much higher carbon footprint and are more responsible for detriments to poorer people because of climate change. Extremely rich people can afford to escape the effects of climate change and pollution, the poor cannot. So if they're responsible for more, they should be more responsible for cleaning up after themselves. This addresses your hurricane zones and sea level rise areas.
3) They travel more and a lot of public infrastructure goes into that (again: roads, air, FAA, airports...)
4) they buy more luxury goods which, again, get to them on public infrastructure (our ocean ports, roads, rail, planes, etc).
5) You'll notice in that paper mentioned in the vox article that healthcare is also used more by the top 10% than the bottom 10% (45% to 0.5%).
6) They rely more on the communications infrastructure (cell phone networks, the internet)
I could keep going, but I'll just end up repeating the paper.
I think you could argue the very wealthy don't rely much on public safety services because they can afford not to live in areas with higher crime rates and can hire their own private security. Possibly also schools.