Generally agree here, but I'm thinking about real scenarios in which I may never be able to recover anything.

One scenario is traveling abroad and having my phone stolen/lost.

For an iPhone, a full backup via iTunes will include the authenticator app data, won't it?

And you'll be printing out emergency passwords when you set up two-factor either way.

It doesn't look like this works with the google authenticator app when restoring to a different device.

For emergency passwords, does that mean you're keeping a printed out copy with you when you travel?

yes.