My understanding is that you put seats rearfacing in the car because the strongest impact in a car accident is likely to come from the front and you want a young baby's spine protected in such an impact.

But on a plane, the main reason to use a car seat is to keep the kid tied down in the event of turbulence. I suppose the greatest impact in a full-on crash is still likely to come from the front,

On take-off and landing, the risk is impact from the front, just like a plane. While cruising, yes, the risk is more turbulence.

In my article, I actually give the tip to turn the seat around for a long flight if it is causing problems with the passenger in front. I passed this by some car seat techs on the web and they weren't thrilled but they didn't flame me.

By the way, "head control" is not the issue. The baby can have the best head control imaginable but the truth is that a baby's head is proportionally much bigger than an adult's. Forward impact for toddlers and babies can cause "internal decapitation" on forward impact. I'm not going to go into that much more!

but the odds of a plane crashing into something and anyone surviving seem so small,

Actually, today your chances are better of surviving a crash. People have panicked and gone the wrong way, etc. who could have survived. My ex-employers would not want me to broadcast this. These details are not released to the press out of respect for the families but trust me, you want to know where your emergency exits are!

If we're worried about forward impacts in planes, why don't the adult seat belts have shoulder harnesses like in cars?

You aren't the first one to ask this. Passengers also asked why we F/A's had the shoulder harnesses. I even saw an amusing comedy sketch ("She's all belting all of herself down while I just go "click"...)

We might be telling our grandchildren how we used to fly when they only had lap belts!