Amps aren't pushed, they are drawn. The generator isn't going to just start melting shit. Whatever gets turned on to utilize power is what will draw amps.
As you started, the wiring is sized for the amperage usage. If you're going to use a generator to run your blender in your kitchen, the 12 awg wire will be able to handle to amount of current the blender draws to operate.
What you wrote is as retarded as saying "your 200 amp panel is going to melt all the wires in your house because the light wiring is only capable of handling 15 amps"
You think the average person wouldn't try to run their entire house by plugging in a generator to a branch circuit?
The breaker would trip.
OK, so that breaker trips, protecting the rest of the house. The branch circuit into which the generator is plugged is still live, and no protective device is between generator and anything else on that branch circuit (except for the generator's own output breaker). Average Joe's family plugs everything into the remaining receptacles on that branch circuit.
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