This is a very good analogy.
Submission isn't something you can (or at least should) feel like you're forcing a woman to do
Submission should feel like "Hey, want me to drive?"
You can't have two people driving a car
The one in the passenger seat can (and probably should) give input on directions, hazards, and of course where the heck you're going, but at the end of the day someone needs to have the final say about the gas pedals and the steering wheel
Asking a woman you barely know "Will you submit to me?" is like "Will you get in my van?"
The answer from her SHOULD be "I don't know yet! Are you a good driver? Where are you even going?"
A major purpose of dating for her is figuring out whether it's worth getting into your passenger seat!
If you're a good driver and you both agree on where to go though, submission should feel easy, it should feel preferable most times
And yeah, this means she shouldn't be yanking the steering wheel away or being an unproductive copilot, backseat driving and constantly offering criticism
But in an ideal world, you don't need to get her to promise to get in the car, put a seatbelt on, etc., it just seems like the obvious choice