It's about being tied to a third-party service. Currently, the one causing you a problem is Apple's. It could just as well be Authy's.
With standard TOTP, you could pull out a paper backup and use it to make any TOTP app on any platform work. But with Authy, you're screwed if they're down.
And it sounds like you're screwed right now because Apple is down. Again, this wouldn't be an issue if you were using standard TOTP.
Meanwhile, if I'd given in and setup 2FA on my company's CloudFlare account, I wouldn't be able to access it right now.
So yes, I have an axe to grind -- with CloudFlare. We pay you $200/month, and the only reason we can still access our account is because I've refused to setup 2FA on it with Authy.
With standard TOTP, you could pull out a paper backup and use it to make any TOTP app on any platform work. But with Authy, you're screwed if they're down.
And it sounds like you're screwed right now because Apple is down. Again, this wouldn't be an issue if you were using standard TOTP.
Meanwhile, if I'd given in and setup 2FA on my company's CloudFlare account, I wouldn't be able to access it right now.
So yes, I have an axe to grind -- with CloudFlare. We pay you $200/month, and the only reason we can still access our account is because I've refused to setup 2FA on it with Authy.