They
are exploring it, it's just slow. Lots of cars now come with "mild hybrid" systems which capture kinetic energy and store it in a supercapacitor, using it to charge the battery and power electrical loads (which are significant these days, with things like electric power steering). Mazda's i-eLoop is one such system (available only on high-end vehicles at additional cost), and Volvo has a similar system, and I imagine some other automakers do too.
The reason you don't see this kind of system everywhere is most likely cost; these systems cost extra. I have the Mazda system on my car; there's a pricey supercapacitor for storing power, plus a pricey DC-to-DC converter under the driver's seat, plus a special high-voltage alternator, plus a special battery. It improves fuel economy by 1-2mpg, which is the other reason you probably don't see them that much: an extra $500 or more in the new price of a car is a lot for an extra 1-2mpg when gas is $2/gallon and everyone's buying SUVs.
Such systems could be done better, but that's likely going to cost even more; to get a more significant improvement you really need to go full-hybrid with a large traction motor, which of course is going to make the vehicle cost even more. Take a look at the Chevy Volt for a good example of what you can achieve here: it's a serial hybrid with a small gas engine with generator plus a traction motor that actually moves the car. It can go 50+ miles without using any gas, which is pretty cool, but when the gas engine comes on (like for long trips) it can only get fuel economy in the low 40s because of the lossiness in the system. On top of that, having all that hardware in the car (engine, generator, motor, battery pack) limits the useful space, and the cost of the vehicle is rather high. Or you can get a Toyota Prius which is a parallel hybrid (engine drives wheels) and gets much better highway economy, but it can't go very far without burning gas and it's pretty expensive for an economy car with very anemic performance.