The TL;DR is that at one point in history, automobile wheels did in-fact use the same construction as bicycles. But the needs of automobiles diverged somewhere in the first half of the 20th Century. And since tires are mounted onto wheels, we need to discuss those first.

I’ve written prior comments here about bicycle wheel/tire fitment and wooden carriage wheel design.

Basically, early horseless carriages used the same wooden wheels that horse-drawn carriages had used for centuries, which have a squared off profile that contacts the ground, sometimes with a steel band – a tyre – to both hold the wheel together and reduce wear on the wheel itself. The only requirements for carriage wheels were to: 1) roll, and 2) bear weight. And using thick wooden spokes, a wagon wheel could achieve those objectives just fine but were really heavy.

When the bicycle was invented in the 1820s, the first iterations used slender variants of wagon wheels, but since 100% of the moving power came from the human rider, this is still unnecessary dead weight to haul around. So bicycle wheels evolved to use very thin spokes, which by the late 19th Century were made of steel in tension, rather than the compressive loads through wood that wagon wheels used. Although steel is heavier than wood, a thin steel spoke has more tensile strength than the same weight of wood has in compression. So overall, it’s a weight savings. Specifically, we say that a bicycle wheel must: 1) roll, 2) bear some weight, and 3) allow for leaning.

The last requirement is crucial for bicycles: they cannot use squared-off carriage wheels, or else leaning the bike will start riding on the edge of the wheel/tire. The solution is simple: round off the contact point so that leaning doesn’t change the profile.

As it turns out, by the 1910s or so, automobiles also realized that wooden wheels were too heavy, and so they also adopted the steel spoked wheel. But they kept the squared off rubber tire, precisely because an automobile does not (normally!) lean during a curve, and instead should be firmly planted on all four wheels. So at this point in history, both automobiles and bicycles are using spoked wheels but just have different shapes for their rubber tires. Great!

But this wouldn’t last: the spoked wheel – which already is a phenomenal structure, essentially being a suspension bridge wrapping upon itself – has one small quirk which bicycles tolerated but automobiles do not. When a spoked wheel is subjected to a straight downward force, the structure distributes the force essentially evenly. But if the force is sideways from the left (ie pushing leftward at the axle), the spokes on the right are heavily stretched but the spokes on the left aren’t. This is uneven loading, that then reverberates from side to side.

This is no issue for bicycles, because they usually lean and so the sideways force is often zero. Sure, a BMX rider can intentionally ride the bike askew, but it’s workable. For an automobile, sideways forces are a regular occurrence, such as during a sharp turn. But also during motorsports where the car is sliding. Spoked wheels can disintegrate when subjected to enough sideways force, which is why cars switched to wheels using sheets of steel rather than spokes. This added weight but was necessary.

Also around this time, cars got very heavy – some would say “land yachts” – and this required making the tire wider to deal with the weight. Since the tire and wheel are the same width in cars, this means wider rims as well. Bicycles have no such issue, because most bicycle tires are “balloon shaped”, and so already are wider than the rim, sometimes almost comically. From a purely materials perspective, making the rim match the tire width does not add strength but does add weight, so cars have to accept that penalty but bikes do not.

In the end, the closest that bicycles and automobiles got was in the early 1900s, and have diverged ever since. Fatbike bicycles and now ebikes pushed the width of tires to some 4+ inches (100+ mm) while touring cars are luxury vehicles meant for long distance, high speed cruising on the Autobahn, and so need wide, high aspect ratio tires.

As for wheel diameter, that’s much simpler to answer: as Jeremy Clarkson noted in the Vietnam Top Gear Special, smaller wheels fall into potholes easier. Bigger wheels roll over them. Automobiles for paved roads use modest diameters, capable of slowly rolling over a 4-6 inch curb to access a driveway. The same diameter on a bicycle would be the 27-inch (aka 700c) or 29-inch class used for road cycling or mountain biking. Whereas smaller folding bikes used exclusively for last-mile commuting can tolerate smaller wheels, because the benefit doesn’t outweigh the diameter penalty when folding it down. All the meanwhile, a motor scooter (eg Vespa) also has small diameter wheels, because they don’t go as fast and urban streets are paved.

For overlanding or bouldering, 4x4 automobiles have some enormous tire diameters and even then, they sometimes have to intentionally reduce the air pressure, so the tire can conform to rock surfaces and thus get more traction. But such tires are wholly inappropriate on a roadway at freeway speeds.