It depends on what your goals are. If you want a system that's only running open-source-built code on your device, but are willing to have your device interact

It depends on what your goals are. If you want a system that's only running open-source-built code on your device, but are willing to have your device interact with devices running proprietary software, then mobile web applications are fine. If you only want to interact with devices and services that are using open source software, then you're likely not to miss e.g. Google Maps application in the first place.