As a followup then, is there a point where it would just be easier/better to use DC power from batteries to spin a DC motor, that is connected to a generator? That would at least be a perfect sine wave 
As you have probably gathered, the situation is a case where grid connection is not available, but the use of regular appliances is wanted.
That's known as a motor-generator set and is the old fashioned way of doing it. Quite often the primary and secondary windings were on one armature, in which case it was known as a rotary converter. Imaging a DC motor, with three poles on the armature, each with a secondary winding, connected to a slip ring. The DC going to the commutator will be converted to three phase AC.
The disadvantages of motor generator sets are: low efficiency, more noise and higher maintenance, as bearings and brushes need to be replaced. The only advantages are they're more electrically robust and can withstand ionising radiation better than electronics.
Nowadays static, semiconductor inverters are used. A boost converter, takes the battery voltage up to the peak voltage of the AC output and an H-bridge converts it to AC. Cheap inverters produce a modified sine wave, whilst more expensive ones use PWM and a filter to give a pure sine wave. The only downsides are they're more vulnerable to over-voltage and ionising radiation, compared to motor generator sets.
If all you want to do is convert one DC voltage to another, use a DC to DC converter.