The primary reason is gasoline is more efficient. It vaporizes easily, burns faster and more completely. On top of that, it is cleaner burning than kerosene.

As I recall the Chrysler turbine cars ran on kerosene (or just about any other combustible) but the turbine engines were not really suitable for automotive use and never went into production. Rover had a turbine program as well, in fact the reason for the P6's unusual front suspension was to make room for a bulky turbine engine that was never actually produced.

It takes too much energy to ignite it , making it too complicated to use. They did make some kerosene engines, but you still needed gasoline to start them and get them going before you could switch to kerosene.