>I wish designers of vehicles - particularly cars, trains and busses, would work to minimize jerk, snap and crackle.
They do.
>Turns out if you minimize those, you get a far more comfortable ride. It matters far more than acceleration.
They know that this is the case. And put a lot of effort into making sure your car has the desired feel.
Besides your comfort these considerations are extremely important for the durability analysis for the vehicle.
>Finite element models of the whole system (tyres and suspension components and flexing elements of the vehicle body and road/track) can quickly allow analysis of the jerk, snap and crackle, and allow tuning of damping and drive system control loops to make a far more comfortable ride.
Finite element simulations are undesirable, they are extremely calculation expensive for those kind of large models and somewhat unsuitable. They are used in crash tests.
For the application you described multi body systems are used, where the car is decomposed into its functional components, which can be modeled either as stiff or flexible. With that you have a reasonably accurate model of a car which you can use to test on a virtual test track.
Basically every competent car manufacturer is doing this.