This has been discussed in other parts of the forum.
There is also a bug opened to Adobe (for iOS, actually), that has been closed as "deferred".
No-one so far has found a solution for making binary files smaller.
I believe this is the price to pay to have a "universal" platform that allows you to develop for different devices with the same code.
I hear you, I just think it'd be nice to have a captive runtime that only adds the necessary libraries the application is requiring, rather than all of them.
I ran my 'hello world' app on my old iPod touch, and it uses 98% cpu to switch between views (each view has one button to go back to a white screen with a few buttons). I love how Flash Builder Structures the View based application, and I hope there's a bright future ahead of it;but for me, if I were to develop with it at this point is to not care about the users who would use my app. By the way, I am a flash developer - so it pains me to say all of this.
from developer news page in Apple
Higher Limit for Over-the-Air Downloads
Mar 20, 2012
Great apps come in all sizes. If you happen to offer a larger app, we’ve made it even easier for App Store customers to get your app wherever they are. We’ve raised the Wi-Fi download requirement from 20 MB to 50 MB so customers can download apps up to 50 MB in size over their cellular data network.
I know this is an old thread, but I'm having the same issue and haven't been able to find a solution. I've built two simple android applications in FB 4.6 and when I package them, the apk files never seem to be less then 9mb. Like you, when I explored the apk, /lib/armeabi-v7a/libCore.so was the largest file. Since you first posted, have you found a way to produce a smaller apk?
We ended up building our app natively. Our final decision came down to a few factors, but we ultimately weren't sure about the performance of our app once all the elements and sections were built out. Given we were under a tight deadline, we weren't confident using Flex would be a good fit for us for a large data driven app. I think it was the right decision, because at the end of the day our app weighs in at about 12 mb.
We are re-evaluating using Flash/Flex for a simple mobile game, which I think will be a bit more successful. The reason for this is that our requirements had changed to having a similar experience on the web as well as mobile devices. Hope this helps!