It's the heat. That's the reason they use wide tires on HP autos and race cars. High performance car and moto tires have a temperature at which they produce the highest adhesion. That's the reason you see racers working to keep their tires warm when they're under the flag. So tire width is calibrated to HP to produce the appropriate surface tread temperature under high performance use.

The lower g's pulled in the economy car example also may be due to tire distortion as well as heat. Cars run with the tire stresses in a different direction that 2 wheelers. Motorcycles are a better example. If you've ever followed a street motorcycle cornering at high speed while running old-fashioned rectangular street tires, you'd see that they also get tire distortion which limits cornering ability. It would be interesting to take low angle video of bicycles cornering at the limit with tires of the same make, but different widths. My guess would be that narrower tires will have less distortion, just from what I've seen when "road racing" street motorcycles in the Alps.

Motorcycle racing tires are triangular in section. I suspect the reason that bicycle tires are not triangular has to do with cost, rolling resistance, and the fact that most of us don't push it like motorcycle racers, riding mostly straight and looking more for good tire wear.