From my interpretation, the play within a play highlights the differences between opinions on love and fidelity as well as the theme of insanity and normality.
Love in the sense that Nick and Lucy represent the young and modern society, that believe in free love whereas the patients are a symbol of the old traditions that emphasises the importance of love. The fact that Lewis, a person from the modern society, not only directs but also participates in the opera shows the contrast between the generalised value of the love decided by the society and the love that is shown to exist in Lewis' life.
Normality in the sense that a bunch of mental patients are shown to act normal because they believe in love and perform an opera about love during the harsh times of the Vietnam war and the free love revolution.
Your right in saying that it does teach Lewis the value of love because you can see a dramatic change in his attitudes and opinions later on in the play. Remember that love doesnt have to be relationship love, it could be family, friendly or even just an object love.
With your last question, I would say definitely, it helps us as the audience to understand the issues better because by Nowra showing a distinctive contrast between the society values (represented by Nick and Lucy) and Cosi Fan Tutte's values it tells us exactly how far apart these two worlds are.
Hope I helped a little atleast!