You should not combine those definitions (1) and (2). They describe different meanings of the same word. Your long single paragraph concentrates on meaning (1) but you have ignored the other possible meaning (2).
We might feel angry about a Western tourist who takes a vacation in a poor country and is blithely unaware of the poverty and disease as he thinks about his next cocktail in the hotel bar, but we do not begrudge a child her happiness as she blithely plays with her toys, even though both uses of the word refer to unawareness of bad things in the world.
Essentially, to be blithe is to be, seemingly, happily unaware of something bad. Whether we frown or smile at it in a person depends on the circumstances.