However the typical piston engine has been replaced quite some time ago. It just hasn't been replaced in cars and trucks. The replacement is the turbine engine (jet engine) which replaced the piston engines in aircraft.
Piston engines still operate in generators, motorcycles, pumps, lawn mowers, etc, etc, etc...
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Placing a scaled down variation of the turbine engine into a car/truck would work very well.
No, it really wouldn't. At least not on a large scale, with one jet and one turbine. Why do you think no-one's done this before?
Logistics. Such setups are fine for generators which don't move (see microturbines), but when you install such a complicated system in a moving vehicle that bumbs and shakes and moves, you get lots of issues, some of which can result in highly unfavorable conditions for the driver. The jet and the turbine each are fine to install on vehicles, but when you combine the two, you have lots of issues. Not to mention the fact that you'd be converting chemical energy to mechanical energy to electrical energy to mechanical energy. It's just not efficient. You're talking about a setup even less efficient than battery-fueled electric car.
Now, if you scale this system down and use a reciprocating shaft to directly produce mechanical energy instead of a turbine to produce electrical energy? Well, that's called a "Fuel-injected internal combustion engine," and it's been around for quite some time. If you DON'T use a reciprocating shaft, and instead simply turn a tubine to produce mechanical energy, you've got a "Rotary Engine."
Wikipedia - Gas Turbines for Electrical Generation (AKA Microturbines)Wikipedia - Fuel Injection(Admittedly, the fuel injected engine bears more resemblance to a rocket than a jet, but in this case, it's all about efficiency.)
Wikipedia - Rotary Engine