Why not handlebars?
Seriously random thought. Was looking at pictures of the earliest automobiles, in the 1885-1910 range. Nearly all of them,
including the steam 'road locomotives', were steered by tillers. The wheel didn't take over until the Model T established it by force of numbers.
The steering wheel makes sense, and it's easy to see its origin in big ships. A geared-down controller for a high-torque rudder, transferred directly to a geared-down controller for a high-torque axle.
But where did the tiller come from? Small sailboats have a tiller, mounted directly on the rudder at the rear of the boat. The automobile tiller looked more like a crank, it was mounted on the front, and it was
often mounted sideways. You would push to turn right and pull to turn left. Completely counterintuitive. Couldn't have been suggested directly by the small-boat tiller. In appearance it closely resembles the speed control on streetcars. But that's not a steering control, because streetcars can't be steered.
At that time,
handlebars would have been the logical choice for a horseless carriage. Handlebars would have been intuitive, familiar,
available, and already associated with wheels. Many of those first experimental autos were built directly from motorcycle parts. The wire wheels, engine and chain drive moved to the four-wheeler, but the handlebars didn't make it. Strange.