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Why do you need to plug this in to your car? take an extension cord along and plug in while you are stopped.
Other option would be a beverage heater that plugs in to the lighter plug, larger truck stops should have them.
To design a lighter plug that could handle the 60+ amps that you would need you would have to have 4 gauge wire or larger and much much heavier contacts in the plug, something along the lines of an oven plug or electric dryer plug, you might as well be asking why you can't plug your arc welder in to your lighter, to me the microwave is the wrong tool to try to use.
For the cost of an inverter that can power your microwave you could even buy a brand new camp stove and the fuel and pots to do all of the heating and cooking you want to do, it would also take up less space.
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