The company you think of as AT&T is really a re-branded SBC and has only been AT&T for 5 years.

The company you think of as a re-branded SBC are reassembled parts of the AT&T that the DOJ broke up in 1984. 4 of the 7 baby Bells and the AT&T long distance company. Bell Atlantic and NYNEX became part of Verizon, and USWest became part of Qwest.

Bell_System_divestiture

Probably the only real obstacle to completely re-assembling the old AT&T would be Gov't objections to AT&T and Verizon combining wireless divisions. Even though they use different technologies, it didn't stop Sprint from buying Nextel.

You're comparing apples and oranges here. In your example you have a low rated wire with a higher rated circuit interrupt. A load that exceeds the capability of the wire will cause it to melt rather than tripping the breaker.

The generator in the parent is a power source, not a power draw, and the circuit interrupt is rated lower. If the power draw from the house is higher than 15 amps, the the circuit will trip disconnecting the draw from the source. Any reasonable generator will throttle back based on load. I don't see how this is different than your primary source, the transmission lines, being capable of considerably higher current than your house mains.

While I personally would want the wiring and transfer switch rated higher than the generator, I doubt it's the invitation to calamity that you imply.