I wonder if there's an equivalent on iOS for andOTP. It puts the backup responsibility on the user in which you can export all tokens to plaintext or password-secured encrypted text. You ultimately put trust in the app maintainers instead of a third party like Authy.
Checkout OTP Auth, which does all that. Very friendly, and very well written with excellent attention to usability details. No net connection unless you enable iCloud saving. No ads even in the free version. Well worth the tiny donation for premium!
I have no connection other than being a happy premium user for around 2 years. By far the best of those I found.