Bloatware on my Phone
Of that 1.73GB, much of it was taken up by apps from Samsung, Google, Virgin Mobile that came with the phone, but I could not remove by default. The solution was to install System app remover. You can then select and remove the apps you don't want.The catch is that in order to use that app, you need root your device. This can be done pretty easily by installing a customer recovery such as TWRP. When you reboot using TWRP, it asks you if you want to root your device. The code is also open source on GitHub.
What is the footprint of the Xamarin example apps?
Shipping Mono and the BCL assemblies inside the app is not free, but it is impressive how much they are able to shrink it down when building in Release configuration. Here are the sizes of the example t-shirt apps. My guess is that the F# app is slightly bigger because it needs to reference FSharp.Core.The C# app is 6.06MB and the F# app is 7.31MB. On my phone, Twitter is 11.35MB, Spotify 13.61MB, and Facebook is 21.75MB. A lot of custom app code can be written before reaching those footprints.
When building in the Debug configuration, it is tuned to use a shared Mono runtime for faster deployments. The shared runtimes are pretty big, but they are for speeding up development round trips.