That's a good point! Airfares can sometimes be cheaper when you book them in advance and under certain conditions. My I am not very familiar with AUD but I guess from a quick exchange rate check that your flight will be around ¥12,000 a return Osaka - Nagoya is ¥12,760. You will probably break even with a JR Pass with traveling to Kyoto and the Airport.
In other words I guess the choice comes down to personal preference between flying and taking the train.
Travel time on the Shinkansen between Tokyo - Osaka is slightly under 3 hours but I think this is about the same with check-in and luggage collection at the airport, not to forget the travel time to and from the Airport. With the Shinkansen you can go to the station 15minutes in advance reserve your tickets and be on your way. Personally I think taking the train would be less of a hassle than taking a domestic flight and planning train tickets around it.
Of course I love traveling by train, so sorry if my advice feels a little partial :)