I never had any chance yet to play with function generators, but I know what they. What I don't see at this moment is their practical usage in digital electronic. For audio I can see it probably for comparison of how good or bad your amp is by comparing the outputs for example, and for digital I saw that some of these function generators can record a digital signal, and later reproduce it on demand and in that case they would act as simulators (right?), but what would be some other practical scenarios?
You are right to say that they are very useful in audio applications. But function generators are also very useful for filter design, Analog-to-digital converters, switched-mode power supplies, and many more.
Here is one very useful example for a power supply unit. Half-bridge, full bridge rectifiers produce a DC output essentially from an AC signal. To raise the AC signal above 0V, you would indeed use a clamping circuit.
Another example I can think of right now would be Analog-to-Digital Converters (ADC). You could have a 10 bits ADC just like what the Arduino Uno's are. Some the analog voltage would be assigned to a bit. For example, 1024 would be 15V and 0 would be 0V. 512 would be 7.5V.
A third example is filters. Low-pass, high-pass, band-pass, and band-stop filters are some you could design and use an AC waveform from the function generator to test it.
Finally, function generators are usually capable of generating a clock signal (square waveform) which can be useful for digital electronics and memory circuits like Flip Flop, Shift registers, and many more. Here is what a function generator can typically generate: