You can actively select an avatar you don’t mind “exposing”. It’s no different than now where I can add whatever character you are posting on.
This is not true because you can’t simply add someone’s battletag and track them. It needs to be mutual. They need to accept the request to even see if you are online or what game you are playing. Unlike right now, someone can silently add you without you even knowing and even contact you in game. That cannot happen with battletags.
This was already discussed in detail.