What's the point of gears in cars? I have a very simple mental model of a car which is applying torque around an axle -- perhaps through a gear train -- onto the wheels. Then KE gained = torque * number of wheel rotations. The car gains a unit of velocity squared for each unit of distance it travels.
I can see that this makes sense for pretty much any car I can think of -- electric motor, gasoline, etc -- which all map some force-producing element onto wheel torque.
Here's what I'm stuck on: what's the point of the geartrain, in this simple model? Why wouldn't I just have my car on the highest gear ratio all the time so it can get fast extremely quickly, since the torque is so high?
I'd ideally like to add pieces to this intuitive model until I can explain everything about cars (or any other machine that moves).
 A: The need for gears depends upon the nature of the propulsion unit and the vehicle being propelled. Some sources of propulsion, such as gasoline engines, have performance characteristics that depend upon the speed at which they run. If you did not have gears then you would not be able to select the optimum engine speed to match a given road speed. For example, driving up a very steep hill requires more power than driving on a level road- to cope with that task you need to increase the power generated by the engine (ie raise its revs), while decreasing the power necessary to maintain the motion of the car (ie reduce its speed). You would not be able to increase engine rpm while reducing speed if the motor were directly coupled to the wheels. There are countless other similar considerations that make gearing essential.
A: 
Why wouldn't I just have my car on the highest gear ratio all the time
so it can get fast extremely quickly, since the torque is so high?

Gears serve to multiply the torque provided by engine at the cost of reducing the rpm provided by the engine.
Input torque * input rpm = Output torque * output rpm
where, Input torque/rpm is the torque/rpm provided by engine
output torque/rpm is the torque/rpm provided to the drive axle
In case of lower gears, the output torque is a higher multiple of input torque, than in case of higher gears and correspondingly the output rpm is a lower multiple of input rpm than in higher gears.
So, lower gears work perfectly when the car is just starting, since at those low speeds, you need low output rpm and high output torque.
Once, the car has gotten to a higher speed, you need high output rpm. So , you shift to higher gears to get the higher output rpm, with the tradeoff that you get a lower output torque.
If your car only had the highest gear, then when you start your car i.e. at lower velocities, the output torque would be too small to get your car moving conveniently. So, it would be a constant pain to drive the car at lower velocities.
You can try it out in any manual transmission car. Try to start the car with the gear set not at 1st gear, but at a higher gear, and see how difficult it is to get the car moving.
