(AnkiDroid has always been run independently, which is good, considering the state of the iOS client, which has always been neglected.)
I don't mind so much that it's paid, given how much use I get for the price, but it sucks knowing it sucks and not being able to help make it better.
It improved my grades so much in college that I spent the 25 bucks as a broke student so I could have it on my second hand iPad. This was before AnkiDroid even existed so it's amazing the price is still the same.
Anki app has an interface for adding/editing cards, and can absolutely be used without AnkiWeb or syncing. In fact, this is how I used it myself for years. I would argue that using AnkiWeb and syncing is an advanced feature for people who got the taste of having own decks and don't want to loose it.