F droid is an app to download or update free or open source software. If you like FOSS, you'd search it before you search the app store.
For some people, yes it can fully replace the app store. For most people, it will replace the app store on some, or maybe even most apps, but there will probably be some proprietary software you need at some point which fdroid won't have.
I noticed many apps in the PlayStore do license checks - even the free/demo versions. They also stated this in the permission list on the store page. However, most of them even ran offline when I checked last time.