Installing some Qt based applications on Android pulls and installs the whole Qt library (temporarily codenamed Necessitas there) which is a dependency. So it does not take 3 seconds at all. Installing shared dependencies when needed is a reasonable practice, otherwise each application will bloat the device with privately bundled libraries.

The fact that Android installation doesn't handle binary dependencies resolution natively it's not an advantage - it's actually a deficiency of design, caused by the original absence of Android NDK and idea of all applications being Dalvik based. Now that Android has an NDK, it becomes a total mess.