It may be safer but it is way less user friendly. If you lose your phone with Google Authenticator (or any competitor), you will lose access to your accounts. You'll need to find your backup codes or go through the process to reset your accounts, which can be very cumbersome. Once someone has to go through this process they won't want to use 2FA anymore, I've seen it happen to many people.
But if you break or lose your cell phone you can just get a new one, and you have access to your 2FA token again immediately. It's much easier for people to work with. Yes it's less secure technically, but that sacrifice is worth it for a lot of people.