The problem in doing things locally is that physical back-ups are risky as well.
No back up will ever be 100% safe, but local back ups are far safer than cloud back ups.
A few years ago a thief broke into my house and stole my computer, tablet, external HD, and other valuables.
If my 2FA backup was there, I would lose all of them (only my phone survived this incident). I lost all my photos, for example, except those in the cloud (90% of them, thankfully).
What about a piece of paper with the codes written down hidden somewhere a thief would never find them? Tape them to the underside of your refrigerator, for example. Or maybe unscrew an electrical socket and hide them inside the wall cavity? There are plenty of places in your house which would a thief would never look.
I would really hate to send my KYC documents to Authy if requested, so they could sell them in the black market or to third party.
Which is why I would never use them. And even if you are never forced to send them your KYC details, they track things like your IP address, geolocation, which sites you are logging in to and when you do so, and share all that with third parties. You are essentially giving them the power to spy on all your crypto-related activities.