Isn't it in the name "TWO FACTOR"? It's supposed to be a separate device and ability to "across devices" comes as an anti-feature for me.
1) If you're not using password manager, then you're probably using same password everywhere, including your 2FA app.
2) If you're storing your 2FA codes in your password manager, then it's not really a 2nd factor. It helps against password leaks from services, not from a password manager leak.
Ability to synchronize encrypted backup is a different story.