Who ever said that hand was the only way to cut wood? If we’re going to go by hand, then we’ve got to compare hand-formed wood to hand-formed plastic–and the plastic won’t win by much. Making a mold or gouging plastic is going to take a lot of time.
If it came down to a race to build identical wheels, one set from wood, one from plastic, one from metal, and one from carbon fiber, from scratch, I’d go with metal being the fastest, and wood being a close second. In probable order of finishing:
Metal: Depending on the metal, cheap(ish), strong, and can be easily worked with given a lathe, mill, or CNC variant of the aforementioned tools.
Wood: Cheaper than metal, can be strong, and could also be done on a lathe, mill, or CNC variant of those two. Just make sure you have wood bits in when you do, cut it a little bit big, and sand it down the last couple thousandths.
Plastic: Once you have the mold (cheapest way to make a lot of identical wheels) or the CNC program (guess what else can be formed on a CNC?), pretty fast. It’s the mold that’ll take a while, if you’re molding. Reasonably strong.
Carbon fiber: High strength to weight ratio–but low strength to wait ratio in this application. Also rather brittle if you hit it wrong. Great for airplane wing spars, not so much for wheels of any sort, and can take a while to shape and set. Also note the cost… The other wheel types are driving merrily around long before the first wheel comes off the first mold.
We’ll assume that everything else is equal for this setup.