The main thing is drag. When you double your speed (with everything else being equal) you quadrupole your drag. You also quadruple your energy (which is part of why it takes much longer to stop from 60mph than it does 80 mph). Thus the drag your engine has to overcome increases much faster than your speed increases. At lower speeds it doesn’t matter much. At highway speeds it will be something noticeable on your fuel economy.
Your school theory is perfect in a vacuum and in an environment with out things like drive train losses. If you are on a flat surface, the main thing that slows down your car when its not powered is wind resistance, and then rolling resistance. Rolling is somewhat minor in comparison. THis is why when you left off the gas at 80mph without the brakes, you slow down pretty quickly, but you can roll for a long time from 10mph before you stop (because the wind resistance is very low at 10mph compared to 80mph)
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