I'm on the same page as you.
chess.com is the only android correspondence chess that I've found. The app is hugely buggy, but just about usable for correspondance chess. Analysis mode I don't bother with on the phone, I just use a computer.
Notifications are pointless, most of the time they are just plain wrong. There is no move waiting when it says there is, and it doesn't notify when there is a move waiting.
If you don't have an internet connection, it won't have cached any games so you can't even think about what move you will make when you get connection again.
The app is very buggy and I too hope chess.com read this and fix it.
I love chess.com. I wouldn't want to join any other chess website. But they're android app is just god awful. Anyone on the same page as me? Its a little better now it used to be worse. I got through less than half of the live games I played on it because it would constantly get disconnected. The only thing its good for is online chess. Even then the analysis mode was completely flawed. Now the latest issue is with the lecture videos. 2 updates ago when you searched for beginner endgames for example, it would bring up intermediate strategy videos. You click on advanced opening videos and it would give you a list of beginner tactics videos. Now the latest bug is when you click and play a certain lecture video it plays a completely different video that you didn't select. Chess.com is nearly perfect. But please fix your mobile app. I dunno if the same bugs exist for the iphone app, but hopefully chess.com reads this and decides to finally try and fix it.