Unless things have changed a bunch, the alternator they used to generate the electric power in the Generac determines the frequency strictly by the RPM of the motor. The frequency and voltage "adjustment" is simply adjusting the RPM of the motor using the engine governor adjustment. Unless the motor is running at the right RPM, you will never have the proper 60hz power frequency.
I'm sure they is done simply because it's the cheapest way to do the job, not necessarily the best or most hi-tech way to do the job.
You should come work for us, I'll show you a few generators that are supposed to work exactly as you have stated above, but for some reason (internal failure) they do not. Our gensets run unattended, meaning when they fail, we are not around to see it and hence require logic safety systems that anticipate things that defy normal operating procedure.
Last summer we had a generator failure that resulted in the it being pulled and replaced. The engine is set to run at 1400 RPM, the well at 1560 and the generator at 1800. This is a monitor only station, so the safety circuit can only log the failure details and shutdown the engine. For the first 200 hours of operation the generator was outputting 485 volts at 60hz and then at hour 207 the voltage dropped off down to 478 and the Hz were down to 53 all the while the input shaft speed was still 1800 RPM. This triggered an alarm log event and an out of spec shutdown. A simple mechanical governor would ignore the real problem and just speed the engine up to reach the desired 485 volts while not realizing there is a major problem inside of the generator.
It easy say this is how it operates, but when you throw in some mechanical failure, watch the sparks fly and toss the normal operating procedure out of the window.