I have to agree with the OP. Benefits to the app is one-click access to important info. The app could have a front page with upcoming trips, including flight status and arrival/departure gates. Maybe one button to see account info (miles, upgrades, etc).

Browsing on my 3g is very slow at times, and to have to wait for the browser to open, load mobile.aa.com, click view reservation (forgot proper name), enter aa number and password, click on the trip i want, memorize the flight numbers, go back to mobile.aa.com, go to flight status, enter first flight number. Repeat for subsequent flights......you get the idea. At least with copy/paste now we can copy the flight number, but it takes way too long to get a few simple pieces of information about my next flights. If the mobile.aa.com site remembered me and had useful information about a trip all grouped together, then I would not need another app.