It takes roughly 1 HP driving a typical alternator to produce 25 amps. Our OEM alternators then cost slightly under 5 HP when charging on full - rare, usually alternator charges about 50-65% most of the time, the rest it's 'freewheeling' and costing next to nothing in terms of parasitic draw on the engine.
It wouldn't matter if this HP came from the crank (engine) or the wheels (which are driven by the engine), the parasitic loss would be the same.
If you wanted to capture the momentum in decelleration and convert it to electricity, you still wouldn't be saving or gaining anything because the engine is still turning and any energy it produces is now lost, or more to the point wasted or unused.
Electric or Hybrid cars gain an advantage here because they can easily shut off their drive motors on decelleration. I suppose you could invent a system to start/stop the engine in an IC car, but anything you'd gain in preserving crank HP or reducing fuel consumption (about 0.1 MPG at 100% charging) would be more than offset by additional wear or diminished service life to the motor (remember 80% of engine wear occurs at startup).
More efficient alternators are the key. Current alternators are about 75% efficient which is really quite good in a mechanical system - an engine is usually only about 25% efficient - Yep that's right...fill-up your 16.9 gal. fuel tank, and only about 4.2 gal. worth of energy ends up actually driving the rear wheels - the rest is lost to mechanical innefficiencies like friction and heat. Most of the energy lost through an alternator comes from mechanical innefficiencies of the belt/pulley system and air resistance to the cooling fins, the rest to heat. Watercooling, as several GM/AC-Delco alternators now use helps some, but mainly extends alternator life as opposed to creating more usable power from the same energy.
So in short, to answer your question:
"Why can't engineering produce a charging system that is driven off the rotation of the wheels to produce a constant electrical current to charge the batteries, like a gas powered welder or generator?"
It can... there's just no advantage in doing so.
