I don't think that's accurate. I've changed phones multiple times and the worst I had to do was find my list of 10 recovery passwords to use one to get in and change the phone I use with Authenticator.

Usually I would just login and add the new phone.

On a personal note, I despise apps like Authy. Every site I've tried to use 2FA on, which didn't use the standard HOTP/TOTP/U2F used an entirely different proprietary app. I have zero interest in having multiple 2FA apps, and even less interest in remembering which app I used on which site. While this clearly isn't Authys fault, its nevertheless a problem.

In other words, please just use standards based 2FA - or SMS/Phone calls.

I just save + encrypt the original QR code somewhere at the time of scanning it.