In classical / romantic harmony, are parallel octaves allowable in left hand chords? When and why? For example, in Chopin's Nocturne Op. 9 No. 2, right at the beginning, there are parallel G-A-G. This is not a case of voice doubling, since the octaves disappear in the second measure.
Yes, here these octava parallels are allowed. (You may mean the rules of strict voice leading in a 4 part-harmony.)
In a piano piece like this in romantic or classic music you don’t mind the rule of forbidden parallels, doubling of voicing can take every where (left and right hand), except this would actually be a 4 part setting.
The piano can play the role of an orchestra as well as a string quartet.