Public airports aren't exclusive to private jets and private schools aren't publicly funded.

Roads aren't exclusive to cars and most of the private schools around here do receive public funding. Just because something is used poorly doesn't mean it's completely useless.

Every single road where pedestrians or alternative modes of transportation aren't allowed and isn't part of a public bus route is car-only infrastructure.

The only road around here that pedestrians and bicycles are explicitly barred from are the freeways, where blocking traffic is very dangerous, but busses, utility vehicles, and industrial vehicles use those all the time.

A highway that busses aren't allowed on?

These exist. You are aware these exist, right?

No, I'm not aware of public roads where it's physically impossible to run a bus line or ride a bike. If a sedan can use it, a bike can use it. If a delivery truck can fit, so can a bus.

I am aware of roads too dangerous to bike on and roads too sparce of destinations to run busses on, but that's because of how roads are used, not a condemnation of roads themselves. If the city decides to add a bus route to a road, no infrastructure needs to be changed. If someone decides to send a charter bus or shuttle, the roads are open to them.