source/output resistance
You are apparently talking about signal generators, not power generators.  The signal can't usually be used immediately at the signal generator output.  That means it has to be somehow transmitted to where it is needed.  Since the shape of the signal is important, the manufacturer of the signal generator has to assume you will want to use a carefully ballanced transmission line for getting the signal from the generator to the load.  As you say, lower impedance is better, so they assume you are using 50 &Omega; coax, which is the lowest impedance commonly available high frequency cable.  Matching the signal generator output to the transmission line impedance allows for the least loss of signal integrity and absorbs reflections at the signal generator end due to any mismatches at the other end.