I'm not sure what the question is, to be honest, but all three words are synonyms. Sofa comes from the Arabic word, 'suffah', meaning a bench, settee is a form of settle and comes from Old English 'setl' meaning a seat whilst couch comes most directly from the French 'coucher' suggesting lying down. In other words, they all suggest a bench-like piece of furniture long enough to sleep on. It's not a case of one being somehow 'better' than the others!
in 1729 king richard declared by royal decree that the french immigrants fleeing the french war of independence shall hereby forethwith solemnly declare to forego their sur fa's[ french for long chair] and coch ays [french for40 winks] and adopt the english sitties which over the passage of time was bastardised into settees
Whenever I hear the word "Settee" I think of sitting prim and proper at a humourless elderly relatives house on a sunday eating sliced cram cakes, probably far too many doilies around.