The only commonly used test gear in general purpose electronics is a multimeter, scope and power supply.
Other gear tends to be indeed more rarely used, but when you need it it really saves you time and effort. A signal generator is only one such non vital but super nice to have when needed kind of gear. Other such gear might be a spectrum analyzer, network analyzer, synthesizer, LCR meter, electronic load, SMU, electrometer, curve tracer etc.. all the way to more exotic things like distortion analyzers, semicoductor analyzers, BERTs, pattern generators, atomic clocks etc..
Getting back to function generators they are mainly useful for providing input stimulus to a circuit under test. Could be anything from testing a transistor to sticking a PWM signal into some module, sweeping the frequency response of something, put test tones trough audio gear etc... Its a very wide application piece of gear, but will certainly not be used as often as a scope.