Should the output impedance of a function generator be high or low?
It depends. If you want to consider your function generator purely as a voltage source, then yes, the output impedance should be as low as possible. It might be helpful to use a separate buffer amplifier for such applications.

On the other hand, it is often useful to connect a function generator (especially an RF generator) to a transmission line, in which case, you want the output impedance of the generator to match that of the line.